A study of tau lepton - University of Birmingham · A study of tau lepton production in t t events...

A study of tau lepton

production in tt̄ events with

ATLAS at the LHC

Neil J Collins

Thesis submitted for the degree of

Doctor of Philosophy

Particle Physics Group,

School of Physics and Astronomy,

University of Birmingham.

September 21, 2011

Abstract

A method is discussed for measuring the tt̄ cross section from tau + jets events in

early ATLAS data. Multivariant techniques were avoided in favour of simple cuts

and the analysis was applied to 26.4pb−1of 2010 data. A cut and count technique

was used to estimate the number of tt̄ events in a window around the hadronic top

mass peak. Subtraction of QCD background from data was performed by scaling

events from a QCD enriched sample by the ratio of events in a sideband region.

With the current dataset a statistical error is expected of the order of ±400% and

a measurement is not feasible at this stage. The systematic error on the tt̄ selection

efficiency was estimated to be ±50%. Simple luminosity scaling established that a

measurement should become possible within the 2011-2013 LHC run. Once ATLAS

has collected between 1 fb−1 and 3 fb−1 of data a fractional error of 20% on the

expected number of signal events could be achieved. Suggestions are made for

reducing the systematic uncertainty on the tt̄ efficiency.

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Author’s Contribution

The nature of modern day particle physics is such that any work is usually of a

collaborative nature. During the production of this thesis I have worked as a member

of the Birmingham ATLAS Group, the L1Calorimeter Trigger Group and at different

times various subsets of the overall ATLAS Collaboration.

This thesis comprises a collection of three separate areas of work; A study of LVL1

tau trigger efficiencies, a study of different tau identification techniques, and a pro-

posed method for making a measurement ot the tt̄ cross section in early ATLAS

data. Each of these studies used data samples which were produced centrally by

the ATLAS collaboration, while the Athena software framework used was also by

necessessity an ATLAS standard.

My contribution involved writing all of the analysis code required to carry out

each of the three studies, together with the software required to post process the

results. The analyses described in each of the three sections, and all the analysis

techniques contained within them, were also my own work. For the tau identification

section this involved development of the single variable cuts, which were compared

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to a standard set provided by ATLAS. In the cross section analysis the cuts and

techniques developed to carry out the measurement were also my own.

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To my family

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Acknowledgements

It has been a privilege to be a member of the Birmingham Particle Physics Group

over the last four years. A substantial part of what has made working in the group

so special is the many people who have featured in that time, to whom I am deeply

indebted and wish to express my thanks;

Firstly, to Peter Watkins, Dave Charlton and Paul Newman, who gave me the

opportunity to study for my PhD in Birmingham during such an exiting period

for the LHC, ATLAS and particle physics in general. Also, to the STFC (formerly

PPARC) and the British taxpayers, who provided the funding to make it possible.

To my supervisor Alan Watson, for his advice, guidance and friendship over the

years, and in particular over the last twelve months. I also apologise for any

headaches and sleepless nights I may have contributed to, with the exception of

those where licenced premises could have also been envolved.

To Chris Curtis who, when not wearing out his P.C. whistle, welcomed me to the

group in the traditional postgrad fashion, and who gave me all the information I

needed for visiting CERN; how to register and where, maps of CERN and Geneva,

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how to use the buses and, most importantly, the location of the best McDonald’s in

Balexert.

To Juergen Thomas, for helping with my Athena problems, and for keeping me

up to date on all things motorsport in Europe, in particular the DTM. To Miriam

and Nigel Watson for their support at deadline time, and to Gilles Mahout and

Richard Staley for breakfasts in R1. Also to Paul Thompson who orchestrated the

departments representation in the Corporate Relay Challenge.

To Mark Stockton and Joseph Lilley for many memorable evenings, and who with

Owen Miller made the RAL Summer School an enjoyable fortnight.

To David Hadley for tea, biscuits and C++, and to Tim Martin for morning coffee.

To Daniel Tapia Takaki for his enduring positivity, even when we couldn’t find a

home for his most expensive blender, and for interesting chats. For this I also thank

Richard Booth and Pablo del Amo Sanchez.

To the many ATLAS students not yet mentioned who have made West 316 the

friendliest office one could ever wish to work in; Benedict Allbrooke, Hardeep Ban-

sil, Andrew Chisholm, Martin Gallacher, Ivan Hollins, Tom McLaughlan and Jody

Palmer. To Steve Bull for organising the traditional summer lunch at The Bell in

Harbourne, and to the other non-ATLAS postgrads I have got to know well; Rav-

jeet Kour, Zoe Matthews, Sparsh Navin, Arvinder Palaha, Plamen Petrov, Richard

Platt, Tony Price, Angela Romano and Patrick Scott.

To Lawrie Lowe for the running repairs on epdt93, and for the laptop loan when my

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netbook self-destructed at the worst possible time.

To all the staff in the Birmingham Particle Group for their support, from ATLAS

group meetings to helping with masterclass computing sessions. Also to my col-

leagues at CERN, particularly within the friendly environment of the L1Calo group.

To Gron Jones for his calming influence before my viva, and my examiners John

Wilson and Richard Batley.

To all those people, from all walks of life, that I am unanble to mention here but

who have taken the time to express an interest in my studies over the years.

Finally, to my parents and my brother Clive, who regardless of my often abrupt

replies to their enquiries, have supported me unequivocally throughout!

Neil Collins - 2011

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If you can dream - and not make dreams your master;

If you can think - and not make thoughts your aim;

If you can meet with Triumph and Disaster

And treat those two impostors just the same;

Rudyard Kipling - 1895

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Contents

1 Top Quark and Tau Physics 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Top Quark Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Standard Model Top Quark Production at Hadron Colliders . . . . . 7

1.5 Top Quark Decay within the Standard Model . . . . . . . . . . . . . 11

1.6 Top Quark Physics at the LHC . . . . . . . . . . . . . . . . . . . . . 13

1.7 Relation to the Higgs . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.7.1 Importance of Studying Taus in Top Events . . . . . . . . . . 14

1.7.2 Tau Decay Classification . . . . . . . . . . . . . . . . . . . . . 18

1.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

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2 The LHC and the ATLAS detector 20

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2 The LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.1 LHC Machine Overview . . . . . . . . . . . . . . . . . . . . . 21

2.2.2 The LHC detectors . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3 The ATLAS Physics Programme . . . . . . . . . . . . . . . . . . . . 27

2.4 ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.4.1 Detector Overview . . . . . . . . . . . . . . . . . . . . . . . . 30

2.4.2 Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.4.3 Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.4.4 Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . 45

2.5 ATLAS analysis tools . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3 The ATLAS Trigger System 53

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.2 ATLAS Trigger Overview . . . . . . . . . . . . . . . . . . . . . . . . 53

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3.3 Trigger Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.3.1 Level 1 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.3.2 Level 2 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.3.3 Event Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.3.4 Trigger Menus, Chains and Event Selection . . . . . . . . . . . 59

3.4 Level 1 Calorimeter Trigger . . . . . . . . . . . . . . . . . . . . . . . 60

3.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.4.2 Cluster Triggers . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.4.3 Jet Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.4.4 Missing ET and Total ET Triggers . . . . . . . . . . . . . . . . 64

3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4 Level 1 Tau Trigger Performance 66

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.2 Trigger analysis details . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.3 Truth matching of taus . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.4 Tau Trigger Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . 70

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4.4.1 Efficiency without application of isolation . . . . . . . . . . . 70

4.4.2 Effect of different isolation cuts . . . . . . . . . . . . . . . . . 77

4.4.3 Comparison of isolation effects for tt̄ and Z → τ τ events . . . 81

4.4.4 Examining the effect of jets for tt̄ events . . . . . . . . . . . . 91

4.4.5 Early Tau Trigger Menu . . . . . . . . . . . . . . . . . . . . . 94

4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5 Hadronic Tau Identification for Early ATLAS Data 100

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5.2 Good Tau Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.3 Tau Reconstruction in ATLAS . . . . . . . . . . . . . . . . . . . . . . 103

5.4 Hadronic Tau Identification by Safe Cuts . . . . . . . . . . . . . . . . 104

5.4.1 Safe Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.4.2 Safe Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.4.3 Calorimeter Only Variable Definitions . . . . . . . . . . . . . . 106

5.4.4 Safe Cut Optimisation . . . . . . . . . . . . . . . . . . . . . . 107

5.5 Evaluation of Calo. Only Safe Cut Efficiencies in tt̄ Events . . . . . . 109

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5.5.1 Efficiency with respect to Monte Carlo . . . . . . . . . . . . . 110

5.5.2 Efficiency with respect to Reconstructed Taus . . . . . . . . . 113

5.6 Calorimeter Only Safe Cut Correlations (Top Events) . . . . . . . . . 122

5.7 Performance Evaluation of a Single Cut Selection . . . . . . . . . . . 127

5.7.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

5.7.2 Production of cut values . . . . . . . . . . . . . . . . . . . . . 128

5.7.3 Isolation Fraction Single Cut . . . . . . . . . . . . . . . . . . . 131

5.7.4 IsolationFraction Summary . . . . . . . . . . . . . . . . . . . . 142

5.7.5 EmRadius Single Cut . . . . . . . . . . . . . . . . . . . . . . . 142

5.8 Overall Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

6 Measurement of the tt̄ Cross Section 155

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

6.2 Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

6.3 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

6.4 LHC Data Periods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

6.5 Object Pre - Selections . . . . . . . . . . . . . . . . . . . . . . . . . . 159

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6.5.1 Tau . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

6.5.2 Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

6.5.3 Missing Et . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

6.5.4 Electron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

6.5.5 Muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

6.5.6 Overlap Removal . . . . . . . . . . . . . . . . . . . . . . . . . 164

6.6 Event Selections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

6.6.1 Choice of tt̄ channel . . . . . . . . . . . . . . . . . . . . . . . 164

6.6.2 Tau + Jets Channel Preselection . . . . . . . . . . . . . . . . 167

6.6.3 Missing ET and event scalar ET . . . . . . . . . . . . . . . . . 168

6.6.4 Transverse Mass Cut . . . . . . . . . . . . . . . . . . . . . . . 170

6.6.5 B Tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

6.6.6 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

6.6.7 Cut flow and purity . . . . . . . . . . . . . . . . . . . . . . . . 172

6.7 Cross Section Measurement and QCD Background Estimation . . . . 174

6.7.1 Hadronic Top Mass Reconstruction . . . . . . . . . . . . . . . 175

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6.7.2 Defining signal region and data driven estimate of QCD back-

ground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

6.7.3 Systematic uncertainty on the efficiency . . . . . . . . . . . . 186

6.7.4 Future prospects . . . . . . . . . . . . . . . . . . . . . . . . . 194

6.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

A 196

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List of Figures

1.1 The three generations of quarks and leptons within the Standard

Model [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Pdf distributions of valence quarks and gluons for Q2 of 175 GeV2 [12] 8

1.3 Diagrams for tt̄ production by gluon-gluon fusion [3] . . . . . . . . . 9

1.4 Diagram of tt̄ production by quark-antiquark anhilation [3] . . . . . . 9

1.5 Mechanisms for single top quark production [3] . . . . . . . . . . . . 10

1.6 Cross sections for production of various physics processes at the TeVa-

tron and LHC as a function of proton - (anti)proton centre of mass

energy [3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.7 Illustration of the general decay for a tt̄ pair, assuming 100% branch-

ing ratio for t → bW+ [8] . . . . . . . . . . . . . . . . . . . . . . . . 12

1.8 Electroweak loop corrections to the W and Z propagators from the

top quark (a and b) and from the Higgs boson (c and d) [3] . . . . . . 15

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1.9 Plot of MW versus Mt showing results from direct and indirect mea-

surements. Lines are shown corresponding to the location of four

different Higgs masses in the plane [9] . . . . . . . . . . . . . . . . . . 16

1.10 Illustration of how a hypothetical charged Higgs boson could be ob-

served in tt̄ decay through couplings to the top quark and tau lepton 17

2.1 Schematic showing the accelerators used to produce 7 TeV protons

at the LHC. 50 MeV protons are produced by the Linac2 and are ac-

celerated sequentially via the PSB, PS and SPS before final injection

and acceleration in the LHC main ring . . . . . . . . . . . . . . . . . 23

2.2 Cross section through one of the LHC main dipole magnets [23] . . . 24

2.3 Illustration of the eight LHC sectors and the locations of the four

major LHC experiments . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.4 The ATLAS Detector [26] . . . . . . . . . . . . . . . . . . . . . . . . 31

2.5 Schematic illustration of a slice through a general particle detector . . 32

2.6 Cut-away view of the ATLAS inner detector (central solenoid not

shown) [26] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.7 Cut-away view showing the complete ATLAS calorimeter [26] . . . . 37

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2.8 A section of the ATLAS EM calorimeter barrel. The three depth sam-

plings can be seen, together with the accordion shape of the electrodes

and the difference in granularity in the three layers [26] . . . . . . . . 39

2.9 Cut-away view showing one half of the ATLAS EM calorimeter (to-

gether with complete endcap) . . . . . . . . . . . . . . . . . . . . . . 40

2.10 Schematic representation of the hadronic tile calorimeter assembly,

with a single module shown for comparison . . . . . . . . . . . . . . . 43

2.11 General arrangement of the LAr forward calorimeter . . . . . . . . . 44

2.12 Illustration of how the eight coils of the ATLAS barrel toroid magnet

are linked together and mounted on the detector feet . . . . . . . . . 46

2.13 View of one of the ATLAS end-cap toroid magnets . . . . . . . . . . 47

2.14 Section throught the side of the ATLAS detector illustrating the ar-

rangement of the muon chambers [26] . . . . . . . . . . . . . . . . . . 48

2.15 Location of the different chamber types within the muon spectrometer 49

2.16 Flow diagram showing the stages required to produce artificially AT-

LAS AOD datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.1 Overview of the ATLAS trigger system [43] . . . . . . . . . . . . . . . 55

3.2 Groupings of trigger towers used in L1Calo electron/photon and tau/hadron

triggers [43] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

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3.3 Groupings of jet elements used in the L1Calo main jet trigger for jet

ET measurement (Jet RoI are hatched) [43] . . . . . . . . . . . . . . 63

4.1 Minimum | 4 R| corresponding to the best matched RoI plotted on

a log scale for both tt̄ and Z → τ τ events (14 TeV centre of mass

energy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.2 Trigger efficiency as a function of the truth visible pT for a tau cluster

threshold of 25 GeV. The turn on curve is for prompt taus in tt̄ events.

No isolation condition is applied . . . . . . . . . . . . . . . . . . . . . 72

4.3 Trigger efficiency as a function of the truth visible pT for four tau

cluster thresholds. The turn on curves are for prompt taus in tt̄

events. No isolation condition is applied (14 TeV centre of mass

energy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.4 Trigger efficiency as a function of the truth visible pT for four tau

cluster thresholds. The turn on curves are for prompt taus in tt̄

events. No isolation condition is applied (7 TeV centre of mass energy) 73

4.5 Trigger efficiency as a function of the truth visible pT for a 25 GeV

tau cluster threshold. The turn on curve is shown for tt̄ and Z → τ

τ events. No isolation is applied and only prompt taus are included

for tt̄ events (14 TeV centre of mass energy) . . . . . . . . . . . . . . 75

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4.6 Trigger efficiency as a function of the truth visible pT for a tau cluster

threshold of 25 GeV. The turn on curve is shown for both the prompt

taus alone and for all the taus in the tt̄ sample. No isolation condition

is applied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.7 Plots of tau trigger efficiency versus truth visible pT, with isolation

applied, for prompt taus in the tt̄ process for a centre of mass energy

of 14 TeV. The left plot shows the effects of 4 and 6 GeV cuts on EM

isolation while the right plot shows the effect of 2 and 5 GeV cuts on

hadronic isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.8 Plots of tau trigger efficiency versus truth visible pT, with isolation

applied, for prompt taus in the tt̄ process for a centre of mass energy

of 7 TeV. The left plot shows the effects of 4 and 6 GeV cuts on EM

isolation while the right plot shows the effect of 2 and 5 GeV cuts on

hadronic isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.9 Plots of tau trigger efficiency as a function of the truth visible pT with

isolation applied for Z → τ τ and tt̄ processes. A range of EM and

hadronic isolation cuts are shown. The samples used had an LHC

centre of mass energy of 14 TeV . . . . . . . . . . . . . . . . . . . . . 82

4.10 Cut by cut comparison of tau trigger efficiency versus truth visible pT

with EM isolation applied for the Z → τ τ and tt̄ processes (prompt

truth taus used for the tt̄ sample) for a centre of mass energy of 14 TeV 83

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4.11 Cut by cut comparison of tau trigger efficiency versus truth visible

pT with hadronic isolation applied for the Z → τ τ and tt̄ processes

(prompt truth taus included for the tt̄ sample) for a centre of mass

energy of 14 TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84


pT with EM isolation applied for the Z → τ τ and tt̄ processes (all

truth taus included for the tt̄ sample) for a centre of mass energy of

14 TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86



(all truth taus included for the tt̄ sample) for a centre of mass energy

of 14 TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.14 Cut by cut comparison of tau trigger efficiency versus truth visible pT

with EM isolation applied for the Z → τ τ and tt̄ processes (prompt

truth taus used for the tt̄ sample) for a centre of mass energy of 7 TeV 89



(prompt truth taus included for the tt̄ sample) for a centre of mass

energy of 7 TeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

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4.16 Cut by cut comparison of τ trigger efficiency versus truth visible pT

with EM isolation applied for dileptonic tt̄ events and mixed semilep-

tonic and dileptonic tt̄ events (truth prompt taus only used for the tt̄

sample). Plots produced for a centre of mass energy of 14 TeV. . . . 92

4.17 Cut by cut comparison of τ trigger efficiency versus truth visible pT

with EM isolation applied for dileptonic tt̄ events and mixed semilep-

tonic and dileptonic tt̄ events (truth prompt taus only used for the tt̄

sample). Plots produced for a centre of mass energy of 14 TeV. . . . 93

4.18 Fraction of events passing the eight LVL1 tau thresholds when run-

ning over a mixture of dileptonic and semileptonic tt̄ events. No

prescaling has been applied . . . . . . . . . . . . . . . . . . . . . . . 95

4.19 Acceptance for the Level 1 items within the proposed ATLAS 1031 cm−2 s−1

tau trigger menu. Plot (a) shows the acceptances before prescaling

and (b) the acceptances after the application of the LVL1 prescales

for a centre of mass energy of 14TeV. . . . . . . . . . . . . . . . . . . 98

4.20 Acceptance for the Level 1 items within the proposed ATLAS 1031 cm−2 s−1

tau trigger menu. Plot (a) shows the acceptances before prescaling

and (b) the acceptances after the application of the LVL1 prescales

for a centre of mass energy of 7TeV. . . . . . . . . . . . . . . . . . . . 98

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5.1 Hadronic tau decays produce a jet with an energy cluster which is

typically narrower than an equivalent QCD jet. Tau candidates can

in principle be distinguished by measuring the width of the shower,

the energy in some defined isolation region around the jet, and by the

track multiplicity within the jet . . . . . . . . . . . . . . . . . . . . . 102

5.2 Distribution of good and fake hadronic taus, normalised to unit area,

for the four variables of the calorimeter only ‘safe cuts’. In these plots

good taus are matched to truth with dR < 0.2, fakes have dR > 0.5

from the nearest truth tau . . . . . . . . . . . . . . . . . . . . . . . . 108

5.3 Selection efficiency comparison between tt̄ and combined Z → τ τ and

A → τ τ events for the calorimeter only tau safe cuts. Comparisons

are split into loose medium and tight cuts (shown by columns running

from left to right), and 1-Prong and 3-Prong hadronic taus . . . . . . 112

5.4 Correlations between the calorimeter only safe cut variables for re-

constructed taus matched to 1-Prong hadronic MC taus (with 4R <

0.2) for the tt̄ sample . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

5.5 Correlations between the calorimeter only safe cut variables for re-

constructed taus matched to 3-Prong hadronic MC taus (with 4R <

0.2) for the tt̄ sample . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

xv

5.6 Correlations between the calorimeter only safe cut variables for recon-

structed taus not matched to 1 or 3-Prong hadronic MC taus (with

4R < 0.2) for the tt̄ sample. This therefore represents the correla-

tions for the background fake taus within the sample . . . . . . . . . 126

5.7 Illustration of setting the single variable cuts. Selection efficiencies

are chosen and then background rejection factors calculated for the

same bin. The right hand plot shows how the bin is selected based

on given signal selection values while the left hand plot shows where

the resulting cut appear on the signal and background distribtions . . 129

5.8 IsolationFraction : Signal and background (fake tau) distributions

and efficiencies for 1-Prong taus in different pT regions . . . . . . . . 133


and efficiencies for 3-Prong taus in different pT regions . . . . . . . . 134


and efficiencies for hadronic taus over the entire pT range . . . . . . . 141

5.11 EmRadius : Signal and background (fake tau) distributions and effi-

ciencies for 1-Prong taus in different pT regions . . . . . . . . . . . . 145


ciencies for 3-Prong taus in different pT regions . . . . . . . . . . . . 146

xvi


ciencies for hadronic taus over the entire pT range . . . . . . . . . . . 153

6.1 Number of tracks associated with reconstructed tau candidates when

either matched to a Monte Carlo truth hadronic tau or not. Plots are

normalised to unit area . . . . . . . . . . . . . . . . . . . . . . . . . . 160

6.2 Charge of reconstructed tau candidates when either matched to a

Monte Carlo truth hadronic tau or not. Plots are normalised to unit

area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

6.3 Correlation between the missing ET and the three jet mass mjjj with

the highest combined pT for Monte Carlo tt̄ events and Pythia QCD

samples. Plots are normalised to 26.4 pb−1 . . . . . . . . . . . . . . . 169

6.4 Correlation between the missing ET and the event scalar ET for Monte

Carlo tt̄ events and Pythia QCD samples. Plots are normalised to

26.4 pb−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

6.5 Transverse mass of the tau and missing ET in non-hadronic Monte

Carlo tt̄ events. Shown in 6.5(a) is a breakdown of all the channels

within the sample while 6.5(b) shows the distribution for tau + jets

events when compared to the modes where no truth hadronic tau is

present. Plots are normalised to unit area . . . . . . . . . . . . . . . 171

xvii

6.6 Cut flow for non-hadronic tt̄ events passing the complete event selec-

tion, broken down into the sample components. Numbers shown are

for the complete Monte Carlo sample totaling 773167 events . . . . . 174

6.7 mjjj distribution for the highest combined three jet pT in non-hadronic

tt̄ events and main backgrounds with the exception of QCD. Nor-

malised to 26.4 pb−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

6.8 Monte Carlo distributions for mjjj possessing the highest combined

three jet pT in non-hadronic tt̄ events for SV0 b-tagged 6.8(a) and

anti-tagged 6.8(b) selections. Plots are normalised to 26.4 pb−1 . . . 177

6.9 Data distributions for mjjj possessing the highest combined three jet

pT after the complete SV0 b-tagged 6.9(a) and anti-tagged 6.9(b) se-

lections but for the requirement 20 < EmissT < 30 GeV. The integrated

luminosity was 26.4 pb−1 . . . . . . . . . . . . . . . . . . . . . . . . . 178

6.10 Schematic diagrams illustrating the variable assignment in the SV0

B-tagged 6.10(a) and anti-tagged 6.10(b) samples for the signal and

sideband regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

6.11 Data distributions for mjjj possessing the highest combined three jet

pT after the complete SV0 b-tagged 6.11(a) and anti-tagged 6.11(b)

selections. The integrated luminosity was 26.4 pb−1 . . . . . . . . . . 181

xviii

List of Tables

2.1 Coverage and granularity of the ATLAS EM calorimeter [26] . . . . . 41

4.1 LVL1 trigger items . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.2 Pure tau trigger items . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5.1 Hadronic 1-Prong tau selection efficiency with respect to reconstructed

taus. Efficiencies are shown for a combined sample of Z → τ τ and

A → τ τ events and for tt̄ events . . . . . . . . . . . . . . . . . . . . 116

5.2 Hadronic 3-Prong tau selection efficiency with respect to reconstructed

taus. Efficiencies are shown for a combined sample of Z → τ τ and

A → τ τ events and for tt̄ events . . . . . . . . . . . . . . . . . . . . 117

5.3 Hadronic 1-Prong and 3-Prong jet rejection factors for inter sample

background events in tt̄ events . . . . . . . . . . . . . . . . . . . . . . 119

5.4 Significance values in tt̄ events of the 1-Prong and 3-Prong hadronic

safe cut selections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

xix

5.5 IsolationFraction pT binned cut values used to select 1-Prong and

3-Prong hadronic taus in tt̄ events. Real cuts give pre-set signal

selection efficiencies, equivalent cut values match the signal selection

efficiency to that for the calorimeter only safe cuts . . . . . . . . . . . 135

5.6 Hadronic 1-Prong tau selection efficiency and rejection factors with

respect to reconstructed taus. Values are shown for a single cut on

IsolationFraction and for the tau calorimeter only safe cuts for tt̄

events. Real IsolationFraction cuts are shown intended to give selec-

tion efficiencies of 70%, 50% and 30% . . . . . . . . . . . . . . . . . . 136



IsolationFraction and for the tau calorimeter only safe cuts for tt̄

events. Real IsolationFraction cuts are shown intended to give selec-

tion efficiencies of 70%, 50% and 30% . . . . . . . . . . . . . . . . . . 137


respect to reconstructed taus. Values are shown for a single cut on Iso-

lationFraction and for the tau calorimeter only safe cuts for tt̄ events

with the IsolationFraction selection efficiencies matched to those of

the equivalent safe cuts . . . . . . . . . . . . . . . . . . . . . . . . . . 138

xx


respect to reconstructed taus. Values are shown for a single cut on Iso-

lationFraction and for the tau calorimeter only safe cuts for tt̄ events

with the IsolationFraction selection efficiencies matched to those of

the equivalent safe cuts . . . . . . . . . . . . . . . . . . . . . . . . . . 139

5.10 Hadronic tau selection efficiency and rejection factors with respect to

reconstructed taus. Values are shown for a single cut on Isolation-

Fraction for tt̄ events. Single cuts are produced for one bin covering

the whole tau pT range . . . . . . . . . . . . . . . . . . . . . . . . . . 141

5.11 EmRadius pT binned cut values used to select 1-Prong and 3-Prong

hadronic taus in tt̄ events. Real cuts give pre-set signal selection

efficiencies, equivalent cut values match the signal selection efficiency

to that for the calorimeter only safe cuts . . . . . . . . . . . . . . . . 147



EmRadius and for the tau calorimeter only safe cuts for tt̄ events.

Real EmRadius cuts are shown intended to give selection efficiencies

of 70%, 50% and 30% . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

xxi



EmRadius and for the tau calorimeter only safe cuts for tt̄ events.

Real EmRadius cuts are shown intended to give selection efficiencies

of 70%, 50% and 30% . . . . . . . . . . . . . . . . . . . . . . . . . . . 149



EmRadius and for the tau calorimeter only safe cuts for tt̄ events with

the EmRadius selection efficiencies matched to those of the equivalent

safe cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150



EmRadius and for the tau calorimeter only safe cuts for tt̄ events with

the EmRadius selection efficiencies matched to those of the equivalent

safe cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

5.16 Hadronic tau selection efficiency and rejection factors with respect to

reconstructed taus. Values are shown for a single cut on EmRadius

for tt̄ events. Single cuts are produced in one bin for the whole tau

pT range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

6.1 Comparison of the number of events in different tt̄ signal channels

passing preselections for tau + jets and tau + lepton events . . . . . 166

xxii

6.2 Number of Monte Carlo signal and background events expected to

pass the selection for a range of integrated luminosities (excluding

QCD backgrounds) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

6.3 Number of events produced in data for the signal and sideband regions

for tagged and anti-tagged selections. Integrated luminosity totaled

26.4 pb−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

6.4 Number of Monte Carlo non-QCD background events expected to

pass the selection for an integrated luminosities of 26.4 pb−1 . . . . . 183

6.5 Projected evolution of S with increasing luminosity, assuming a sim-

ple upscaling of the values for TS, TB, AS and AB . . . . . . . . . . . 185

6.6 Fractional uncertainty on the efficiency as a result of a ±5% shift in

the jet energy scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

6.7 Fractional uncertainty on the efficiency for two different generator

and PDF combinations . . . . . . . . . . . . . . . . . . . . . . . . . . 189

6.8 Fractional uncertainty on the efficiency as a result of a shift in the

top quark mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

6.9 Fractional uncertainty on the efficiency as a result of a shift in the

b-tagging efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

6.10 Fractional uncertainty on the efficiency as a result of a ±10% shift in

the tau selection efficiency . . . . . . . . . . . . . . . . . . . . . . . . 191

xxiii

6.11 Systematic uncertainties on the efficiency ε for selecting tt̄ events via

the method described . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

A.1 Calorimeter only safe cut values for identification of 1-prong hadronic

taus [53] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

A.2 Calorimeter only safe cut values for identification of 3-prong hadronic

taus [53] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

xxiv

Chapter 1

Top Quark and Tau Physics

1.1 Introduction

Particle physics strives to explain the fabric of the known universe by understanding

the smallest building blocks from which it is constructed. The Standard Model,

considered one of the greatest triumphs of 20th century science, achieves this by

describing a series of elementary particles and how they interact. Futhermore, it

has made accurate predictions which have subsequently been verified by experiment.

This chapter introduces the Standard Model, together with a more detailed coverage

of the properties of the top quark, the most recently discovered elementary particle.

The relationship between the top quark and the tau lepton is also covered, notably

how it provides a possible window on new physics beyond the Standard Model.

1

1.2 The Standard Model

The Standard Model is the label applied to the theory which describes the current

understanding of particle physics. The theory comprises a series of elementary

particles and the forces which combine to produce the known matter seen in the

universe.

Elementary particles within the Standard Model are refered to as fermions. Fermions

have half-integer spin and are divided into two types, known as quarks and lep-

tons [1]. Both types are currently known to each comprise six fundamental particles

which are separated into three groups of pairs of particles. Equivalent particles in

these three ‘generations’ have identical properties with the exception of their masses.

Generation III particles are more massive than generation II particles, which in turn

are more massive than those in generation I (the constituents of all known stable

matter in the universe). The arrangement of the fermions within the generations is

shown in Fig. 1.1 [2];

A distinction exists between the arrangement of the quarks and leptons within the

three generations. In the case of quarks, six distinct versions refered to as flavours

exist and are known as up (u), down (d), charm (c), strange (s), top (t) and bottom

(b) [1]. The three ‘up type’ quarks have an electric charge of +2/3 while the three

‘down type’ quarks have a charge of −1/3 [2]. In contrast each generation has one

massive lepton of charge -1 and one lepton neutrino with zero charge1. Consequently

there are only three lepton flavours which are labeled as electron(e), muon(µ) and

1Electric charge is defined in units of the electron charge [2]

2

Quarks

u

d

c

s

t

b

Leptons

νe

e

νµ

µ

ντ

τ

Figure 1.1: The three generations of quarks and leptons within the Standard Model [2]

tau(τ) [2]. For both quarks and leptons an equivalent set of antiparticles exist which

have the same properties as the particles but with the sign of all charges, for example

the electric charge, plus certain other quantum numbers reversed [1]. Quarks carry

a property known as colour charge (red, green or blue), whereas leptons do not.

Colour is a quantum number that allows for interactions with the strong force (in

an analogy to the interaction of the electric charge with electric fields) but which

is not observed in nature. This requires that quarks can only exist in a composite

bound combination with overall zero colour. These bound states can either comprise

three quarks (one of each colour), refered to as baryons, or alternatively a quark and

antiquark pair (one with colour and the other with anticolour), known as mesons [2].

The leptons by contrast only exist as isolated particles.

Of the four known fundamental forces, the effect of the electromagnetic, weak and

strong forces on the elementary particles are fully included in the Standard Model.

3

These forces are modeled by quantum field theories where the interactions between

the particles are performed by the exchange of spin 1 gauge bosons [1]. For the

electromagnetic force, which acts only on electrically charged particles, the exchange

particle is the massless photon and the relevant area of the theory is refered to as

Quantum Electrodynamics (QED) [2]. In the case of the strong interaction, the force

is carried by one of eight gluon states. While gluons do not carry electric charge,

they do possess colour charge. Consequently, gluons interact with quarks (it is the

gluons that bind the quarks into baryons and mesons) and can also self-couple, but

do not couple to leptons. The area of strong interactions is described by Quantum

Chromodynamics (QCD) [2]. Finally, the weak force is accounted for within the

Standard Model by exchange of the massive Z0 and W± bosons [1]. These can self-

interact but unlike the gluon do not carry colour charge. All fermions do however

have weak charges. It is via exchange of the W bosons that quark flavour change is

allowed to take place as occurs in beta decay [1].

The field theory is structured around a gauge symmetry described as being

SU(3)C × SU(2)L × U(1)Y [2]. Within this arrangement QCD and the gluons are

covered by SU(3)C alone. In contrast, QED and the weak force (with their associated

bosons) are together covered by SU(2)L × U(1)Y and so are therefore usually refered

to as the combined electroweak force [2]. The theory as a whole is required to be

gauge invariant [3]

A currently unresolved area of the Standard Model is providing an explanation for

why the various particles have their observed masses. This aspect of the theory

4

must explain why the Z0 and W± bosons are massive but the photon is not, and

also accommodate the mass hierarchy seen in the fermions, while at the same time

ensuring the theory remains gauge invariant. The part of the Standard Model

intended to address this is the Higgs mechanism. Within the Higgs mechanism four

scalar fields are added to the theory which are arranged such that the scalar potential

has a non-zero Vacuum Expectation Value [1] (the starting point for calculations

made using perturbation theory). When combined with the rest of the theory, this

allows the bosons and fermions to aquire mass, whilst also requiring the existence

of an electrically neutral spin zero scalar particle; the Higgs boson. Unobserved to

date at the LEP and TeVatron colliders the search for the Higgs is a major goal of

the Large Hadron Collider, while its discovery (or otherwise) would be a significant

landmark in particle physics.

1.3 Top Quark Physics

The top quark is the heaviest within the Standard Model, forming the weak isospin

partner of the bottom quark in the third quark generation [4]. Fundamental param-

eters of the Standard Model associated with the top quark are its mass mt and the

CKM (Cabbibo-Kobayashi-Maskawa) mixing matrix elements, Vtb, Vts and Vtd [5].

All other Standard Model top quark properties are fixed because they must match

those of the up and charm quarks in the first two generations.

Since the discovery of the top quark in March 1995, by the CDF and DØ teams at

5

the Fermilab TeVatron proton-antiproton collider, all direct measurements prior to

2010 have used the 104 top quark events recorded at that accelerator [6]. The first

estimate of the top quark mass came from measurements made on twelve events

observed in 1994 [7], before the top discovery was confirmed. The events suggested

a top mass of;

mt = 174 ± 10+13−12 GeV (1.1)

and were fully analyzed in [8]. Subsequent analysis using the complete 100 pb−1

Run I Fermilab TeVatron data combined with further data from Run II sets the

current value of the top quark mass from direct observation as [9];

mt = 172.0 ± 0.9 ± 1.3 GeV. (1.2)

The matrix element Vtb is known less accurately. Results from single top observation

at CDF and DØ currently indicte a value for Vtb of [9];

|Vtb| = 0.88 ± 0.07. (1.3)

During 2010 the ATLAS experiment at the LHC collected approximately 46 pb−1

of data. Coupled to the estimated cross section for tt̄ pair production of 160 pb

(NLO) [10] at a proton-proton centre-of-mass energy of 7 TeV, approximately 7300

tt̄ events should have been produced. Analysis of these data was ongoing at the

6

time of writing.

1.4 Standard Model Top Quark Production at Hadron

Colliders

Within the Standard Model, top quarks are produced in two different ways at the

LHC. These are as a tt̄ pair via QCD processes (the strong interaction), or singly

by electroweak processes [11]. For mass measurement tt̄ pair production events are

more convenient. Single top events are useful when measuring the matrix element

Vtb or examining the W-t-b vertex properties [6].

An important aspect of hadron colliders is that the colliding particles are quark

composites bound together by gluons. As a consequence, the production mechanism

observed in QCD processes depends on the type and energy of the colliding particles.

Within the parton model theory, hadrons are treated as being a collection of quasi-

free quarks and gluons [1]. Each parton i within the hadron is taken as carrying

a momentum pi in the prescribed longitudinal direction (this would be taken as

the beam direction in a hadron collider) and so possess a fraction xi = pi/p of

the overall momentum p of the hadron in that direction [1]. Parton Distribution

Functions (PDFs) are used to describe the probability density for finding a parton

within a hadron possessing a momentum fraction xi [1], when considered for a given

scale Q2 [3]. When dealing with tt̄ production the scale is often taken to be of

the order Q = mt, where mt is the top quark mass [1]. Fig. 1.2 shows the Parton

7

Distribution Functions (PDFs) of the valence quarks and gluons for Q2 of 175 GeV2.

Figure 1.2: Pdf distributions of valence quarks and gluons for Q2 of 175 GeV2 [12]

For a symmetrical collider, assuming the colliding partons are of similar xi, the value

of x which is accessible during the collision can be expressed as x ≈ mt/√

(s) [1].

For the LHC operating in 7 TeV mode this has a value of 0.05 (0.025 when in

14 TeV configuration). From Fig. 1.2 it can therefore be seen that at the LHC QCD

top quark pair production typically occurs for up to small values of the momentum

fraction x [3] and so is dominated by gluon-gluon fusion processes [13]. The three

lowest level Feynman diagrams for these processes are given in Fig. 1.3.

In contrast, the Fermilab TeVatron 1.96 TeV centre of mass energy collisions are

only able to probe down to values of x of approximately 0.2, which is above the

8

g

g

t

t

g

g

t

t

g

g

t

t

Figure 1.3: Diagrams for tt̄ production by gluon-gluon fusion [3]

region where the gluon PDF begins to dominate. When added to the fact that the

TeVatron is a proton-antiproton machine, top quark pair production is dominated by

quark-antiquark annihilation as shown in Fig. 1.4, contributing 85% of events [14].

q

q

t

t

Figure 1.4: Diagram of tt̄ production by quark-antiquark anhilation [3]

Electroweak single top production occurs within the Standard Model via three meth-

ods; s-channel, t-channel (or W-gluon reactions) and Wt production. The various

means by which single top quarks are expected to be produced at the LHC are

shown in Fig. 1.5.

A further aspect to consider with regards to top quark production is the variation of

the cross section as a function of the centre-of-mass energy of the collision. Fig. 1.6

shows cross sections as a function of centre-of-mass energy for a series of different

9

g

b

b

t

W

Wt production’q

q

W

b

t

s-channel

q’

g

q

b

tWb

t-channel

Figure 1.5: Mechanisms for single top quark production [3]

processes. For tt̄ production the cross section is predicted to be approximately 160pb

for a proton-proton collision energy of 7 TeV [13], which rises to 833pb at 14 TeV

(at NLO) [3].

Figure 1.6: Cross sections for production of various physics processes at the TeVatron and

LHC as a function of proton - (anti)proton centre of mass energy [3]

10

1.5 Top Quark Decay within the Standard Model

Quark decays within the Standard Model occur via flavour change through the weak

interaction, by exchange of W+ and W− bosons. A quark of charge +2/3 (u, c, t)

is always transformed to a quark of charge −1/3 (d, s, b) and vice versa. The top

quark can decay to any of the three charge −1/3 quarks via W+ boson exchange, in

accordance with the CKM mixing matrix [1]. The CKM matrix elements also define

the relationship between the weak and mass quark eigenstates [1].

The CKM matrix is defined as being unitary (assumed for three quark genera-

tions [3])and the elements within it squared are proportional to the probability of

the corresponding decay occuring [15]. The matrix elements define how strongly the

W boson couples to the various quarks. Non zero matrix elements correspond to

decays that may occur, while matrix elements that are zero correspond to decays

which cannot (no non-zero elements are known to exist, although some are very

small). Therefore the matrix elements of the Standard Model define which decays

can occur, which cannot and which are suppressed.

The allowed top quark decays; t → bW+, t → sW+ and t → dW+, are represented

in the CKM matrix by the elements |Vtb|, |Vts| and |Vtd|. Assuming |Vtb| = 1,

measurements of the B0s combined with lattice QCD calculations give estimates of

|Vts| = (38.7 ± 2.1) × 10−3 and |Vtd| = (8.4 ± 0.6) × 10−3 respectively [9]. A direct

measurement without assuming unitarity gives a value of |Vtb| = 0.88 ± 0.07 [9].

The t → bW+ decay therefore dominates, while the t → sW+ and t → dW+ decays

11

are heavily suppressed, possessing expected branching ratios of approximately 0.1%

and 0.01% [6]. The top quark undergoes a weak decay and is expected to do so as

an isolated quark because the top lifetime (approximately 10−24 s) is shorter than

the timescale required in QCD for hadrons to form (in the order of 10−23 s [8]).

For QCD top production, where a top and an antitop are produced, the antitop will

decay following the same process as the top, but with the relative antiparticles. The

antitop will therefore decay to an antibottom quark and a W− boson.

Assuming 100% decay of the top to a bottom quark and W boson, the decay sequence

of a tt̄ pair is identified by the decay of the W+ and W− bosons produced by the

decaying top and antitop [8]. Fig. 1.7 shows the generalized standard decay of a tt̄

pair.

g

g t

tb

-W

b

+W

, q’-l

q , lν

, q’lν

q , +l

Figure 1.7: Illustration of the general decay for a tt̄ pair, assuming 100% branching ratio

for t → bW+ [8]

Each of the W bosons in a tt̄ event may decay to a qq̄ pair or to a lepton and neutrino.

Consequently there are four classes of tt̄ pair decays; single lepton events, dilepton

events, fully hadronic events and ‘tau plus X’ events. Differences in the behaviour of

12

the tau compared to the electron and muon is the reason that tt̄ events containing

taus are classified separately, see 1.7.2. The branching ratios for these processes are

30%, 5%, 45% and 20% respectively [6]. The tau+X events are themselves divided

in a similar way into tau+jets, tau+lepton and ‘two tau’ events.

Irrespective of how the W+ and W− bosons decay, the bottom and antibottom

quarks produced will behave the same way in each case. The bottom quark lifetime

is longer than that required for hadrons to form by the strong interaction. Con-

sequently, confinement forces the bottom quark to undergo hadronisation. One of

the hadrons produced contains the original bottom quark, usually as a B-meson.

A cone of hadrons known as a jet (in this particular case a b-jet) is formed, the

axis of which propagates in the same direction as the bottom quark was originally

travelling. Any quarks produced from the W decays hadronise in the same way into

light quark jets.

1.6 Top Quark Physics at the LHC

The number of top quarks to be produced each year at the LHC will enable a wide

range of top quark physics to be carried out. Key areas to be studied include mea-

surement of the top quark mass, searches for non Standard Model heavy resonances,

study of electroweak single top production (including measurement of the matrix

element Vtb and determination of the W-t-b vertex properties [6]), examination of

top quark decays, branching ratios and couplings, top quark charge determination,

13

searches for flavour changing neutral currents (FCNC) and examination of top quark

spin correlations. These have been fully described elsewhere, for example in [1] and

[3].

1.7 Relation to the Higgs

The electroweak gauge bosons, Higgs boson and the heavy quarks are all interlinked

through high order electroweak processes. Fig. 1.8 shows how the top quark and the

Standard Model Higgs boson can occur in loop diagrams in relation to the W and Z

bosons[3]. By making accurate measurements of electroweak processes, it is possible

to extract an estimate of the Standard Model Higgs mass. Adding in the measured

top quark and W boson masses allows the Higgs mass to be further refined. Fig. 1.9

illustrates where four different values of the Standard Model Higgs boson would lie

in a plot of MW versus Mt, and how the measured quantities therefore suggest the

presence of a relatively light Higgs [3].

1.7.1 Importance of Studying Taus in Top Events

Tau final states are predicted for a number of physics processes, both within and

beyond the Standard Model. Assuming the Standard Model, measurement of the

tt̄ production cross-section with tau+jets and tau+lepton events provides a cross

check of measurements made in the electron and muon channels. Tau production has

been predicted as a possible signature for certain beyond the Standard Model Higgs

14

Z

t

t

Z

(a)

W

t

b

W

(b)

h

(c)

h

(d)

Figure 1.8: Electroweak loop corrections to the W and Z propagators from the top quark

(a and b) and from the Higgs boson (c and d) [3]

15

Figure 1.9: Plot of MW versus Mt showing results from direct and indirect measurements.

Lines are shown corresponding to the location of four different Higgs masses in the plane [9]

bosons, various supersymmetry (SUSY) models and other potential new physics [16].

The Standard Model Higgs mechanism consists of only one scalar field doublet [1].

Extensions to the Standard Model however can propose the existence of two Higgs

doublets, refered to as Two Higgs Doublet Models (THDM) [1], which come in two

types. Type I THDM only allow one doublet to couple to fermions, but in type

II THDM (the simplest of which is the Minimal Supersymmetric Standard Model

or MSSM) one doublet couples to up type quarks or neutrinos, while the second

couples to down type quarks or charged leptons [1]. In both cases, five Higgs bosons

are predicted as opposed to one in the Standard Model, comprising three neutral

Higgs’ h0, H0 and A0, plus a pair of charged Higgs’ H± [1].

The massive nature of the tau lepton, when compared to electron and muon masses,

means that should a light charged Higgs boson exist, it would be expected to couple

preferentially to the tau [17]. Fig. 1.10 demonstrates how such a coupling can occur

in a tt̄ decay, where the charged Higgs (with mass smaller than the difference between

16

the top and b quark masses) replaces one of the two W bosons in the decay. How

such a charged Higgs would decay depends on the value of tan β, which is the ratio

of the vacuum expectation values in the two Higgs doublets [1];

tanβ =v1

v2

(1.4)

Such a charged Higgs is predicted in the MSSM to couple strongly to the massive

top quark for values of tan β & 70 and . 1 [1]. For tan β > 1 the H+ → τν channel,

as shown for one of the top quarks in Fig. 1.10, is predicted to feature significantly

(rising to a branching fraction close to 100% for tan β > 5) thus making tops

decaying to taus an ideal search candidate [1]. For tan β < 1 H+ →cs̄ dominates

while the t→H+b production is minimised for tan β close to 1. The existence of a

charged Higgs in the region preferable for tau production would manifest itself as an

enhanced branching fraction for t→bτν when compared to the Standard Model [4].

g

g t

tb

-W

b

+H

, q’-l

q , lν

, cτν

s , +τ

Figure 1.10: Illustration of how a hypothetical charged Higgs boson could be observed in

tt̄ decay through couplings to the top quark and tau lepton

17

1.7.2 Tau Decay Classification

The tau is unique in the lepton sector of the Standard Model. Due to its mass

of mτ = 1776.99+0.29−0.26 MeV [18] it is the only one of the three leptons which is

allowed to decay either leptonically or hadronically [19]. Consequently taus are

classified in accordance with whether they decay to leptons (with branching fractions

of (17.36 ± 0.05)% to µ−ν̄µντ , (17.84 ± 0.05)% to e−ν̄eντ , (3.6 ± 0.4)% to µ−ν̄µντγ

and (1.75±0.18)% to e−ν̄eντγ [18]) or hadrons (with a combined branching fraction

of approximately 65%).

For the case where the taus decay into hadrons a further degree of classification is

applied in relation to the number of charged mesons (dominated by pions) initially

produced. Decays where only one charged pion or kaon is produced are refered

to as 1-Prong and comprise mainly of τ → π±ν and τ → nπ0π±ν, accounting

for 22.4% and 73.5% of the decays respectively [19]. Likewise, decays producing

three charged pions or kaons are refered to as 3-Prong and consist mainly of the

modes τ → 3π±ν and τ → nπ03π±ν, which make up 61.6% and 33.7% of the total

number of 3-Prong taus [19]. Note that in both cases nπ0 signifies the production

of any number of neutral pions. Decays to 1-Prong and 3-Prong modes occur with

relative fractions of approximately 85% and 15% of the total hadronic branching

fraction respectively [9]. Further 5-Prong and 7-Prong hadronic decays can also

occur with negligible branching ratios, but due to their higher track multiplicity are

more difficult to distinguish from conventional non-tau jets. The branching fraction

to modes containing K± is small, of the order of 1% in both 1-Prong and 3-Prong

18

cases. These modes are indistinguishable to the ATLAS detector from the equivalent

π± decays [19].

1.8 Conclusions

Within this chapter the Standard Model of particle physics has been introduced

and its main features described. Further detail was provided on the top quark,

including its decay mechanism and the production methods accessible at hadron

colliders. Current experimentally measured values of the top quark mass and the

CKM matrix element Vtb were given. The relationship between the top quark and the

as yet undiscovered Standard Model Higgs boson was also noted. A brief explanation

was then given as to why, for certain values of tan β, top quarks decaying to tau

leptons can provide a probe for light charged Higgs bosons proposed by certain two

Higgs doublet models. Finally, the decay modes of the tau lepton were described

and their appropriate branching ratios quoted.

19

Chapter 2

The LHC and the ATLAS detector

2.1 Introduction

Constructed under the French-Swiss border and assembled over a decade, the Large

Hadron Collider (LHC) is often described as the largest machine ever made. Com-

mencing operation in 2010 the LHC is the world’s most powerful particle collider,

producing data which are analysed by some of the most sophisticated detectors pro-

duced to date. Within this chapter can be found a brief overview of the LHC and

how it operates. The ATLAS detector is described together with its constituent

components, while the physics goals and their demands are mentioned. In addition

the ATLAS data structure is also summarised.

20

2.2 The LHC

The Large Hadron Collider (LHC) accelerates and collides beams of protons or Pb

nuclei in the highest energy particle collisions ever produced artificially. The LHC

has been constructed at the CERN laboratory in the 27 km circumference tunnel

formerly used to house the LEP and LEP II electron - positron colliders between

1989 and 2000. Designed to produce 14 TeV centre of mass energy proton-proton

(pp) collisions at a luminosity of 1034 cm−2s−1 [20], during 2010 the LHC operated

in proton-proton mode with a centre of mass energy of 7 TeV and up to a maximum

luminosity of approximately 2 × 1032 cm−2s−1. Comprising a mixture of commis-

sioning and physics running, a total of approximately 46 pb−1 of proton-proton data

were collected during this period [21]. Fermilab’s TeVatron proton-antiproton (pp̄)

collider, the most powerful machine previously available, has a Run II centre of mass

energy of 1.96 TeV and luminosity of approximately 1032 cm−2s−1 [1].

2.2.1 LHC Machine Overview

At the LHC, counter rotating beams of protons are accelerated to a maximum of

7 TeV (3.5 TeV during 2010) and brought together to collide at the centre of the

four LHC detectors. At the mimimum bunch spacing configuration collisions are

produced every 25 ns. Each bunch will contain up to 1.15 × 1011 protons and will

have an RMS length of 0.075 m and a nominal diameter of approximately 1 mm.

However, the bunch diameter is further reduced to 16 µm at the collision points. At

21

full intensity and design energy, each LHC beam will contain 2808 proton bunches

25 ns apart and would hence have a beam energy of approximately 362 MJ.

In order to produce high energy proton beams, a series of different accelerators are

used to provide and then ramp the particle energy up in stages, culminating in

the LHC main ring. To begin with, the CERN Linac2 linear accelerator is used to

produce 50 MeV protons which are then fed into the Proton Synchrotron Booster

(PSB). The protons are accelerated to 1.4 GeV in the Booster and are then injected

into the Proton Synchrotron (PS) itself where they are further accelerated to 26 GeV.

From the PS, the protons pass into the Super Proton Synchrotron (SPS) and are

taken up to an energy of 450 GeV before passing down two tunnels, built to link the

SPS and the LHC, and filling the two separate LHC beam pipes. Final acceleration

of each beam to the desired energy, of up to 7 TeV, occurs within the LHC itself.

The chain of accelerators is show in Fig. 2.1

The two proton beams are accelerated within the LHC by strong electric fields

provided via radio frequency (RF) cavities (energy is transfered from the radio waves

in the cavity to the particles in the beam) and steered around the ring by powerful

dipole magnets. As a pp collider, both LHC beams possess the same charge. To keep

two counter rotating proton beams travelling around the LHC ring, the directions

of the magnetic fields applied to the two beams must be exactly opposite so that

each beam is bent the correct way. Beams are contained in separate pipes with a

magnetic field applied independently to each one. The beam energy limit obtainable

at the LHC is determined by the maximum bending power of these magnets to keep

22

Figure 2.1: Schematic showing the accelerators used to produce 7 TeV protons at the

LHC. 50 MeV protons are produced by the Linac2 and are accelerated sequentially via

the PSB, PS and SPS before final injection and acceleration in the LHC main ring

protons travelling around the tunnel (of approximately 4.5 km radius). To achieve

a maximum proton beam energy of 7 TeV, and hence a maximum centre of mass

energy for a symmetrical collider of 14 TeV, 1232 superconducting dipoles producing

a field of 8.4 T are required, the most powerful ever made. For the LHC special

two-in-one magnets have been developed which allow the two beams of protons, in

23

separate beam pipes, to be dealt with by one unit [22]. In the design, there are two

magnet windings, one for each beam pipe, but there is a common support and yoke,

and the whole ensemble is housed in a single cryostat. The magnets are cooled

to 1.9 K using superfluid helium and the superconductor used is NbTi. Fig. 2.2

shows a cross section through one of the main accelerator dipoles. Manufacturing

the magnets in this way was cheaper than producing separate items for each beam

and also took up less space in the machine tunnel previously occupied by the single

beam pipe of LEP.

Figure 2.2: Cross section through one of the LHC main dipole magnets [23]

In addition to the accelerator magnets, there are a number of others which add up to

more than 1700 overall. Most notable of these are the eight sets of focusing magnets

located in pairs either side of the four LHC collision points.

In general the LHC is described as a ring, however in practice it is comprised of

eight curved sections and eight straight sections. The eight LHC points are situated

24

on the straight sections, which are each 528 m long, with their locations as shown

in Fig. 2.3.

Figure 2.3: Illustration of the eight LHC sectors and the locations of the four major LHC

experiments

Four of the eight points (1, 2, 5 and 8) house the LHC experiments as discussed later

and are the only places where collisions take place. In addition to being experimental

areas, points 2 and 8 are also where the two beams enter the LHC from the SPS.

At points 3 and 7 are located beam cleaning magnets to keep the two LHC beams

collimated. Point 4 is where the LHC RF (radio frequency) beam control system

is found, which has been covered in detail elsewhere [24]. Finally point 6 (the

former location of the LEP OPAL detector) is the site of the beam dump, where

the beams can be removed from the LHC ring and disposed of in a controlled way

via a combination of ‘kicker’ and septum magnets [20].

25

2.2.2 The LHC detectors

The LHC has four principal experiments situated around the accelerator ring. These

are ALICE [25], ATLAS [26], CMS [27] and LHCb [28] and their relative under-

ground locations are illustrated by Fig.2.3. In addition there are two further exper-

iments called TOTEM [29] and LHCf [30].

ATLAS (A Toroidal LHC ApparatuS) and CMS (Compact Muon Solenoid) are

situated at points 1 and 5 on the LHC ring respectively. Housed in caverns built

from scratch for the LHC they are the largest particle physics collider detectors

ever built; ATLAS is the largest with respect to volume and CMS with respect to

mass. Both are general purpose detectors intended to look at all aspects of LHC

physics [31] with a bias towards pp running but also some ability to study Pb-Pb

collisions. ALICE (A Large Ion Collider Experiment) is located at point 2 in the pit

which formerly contained the LEP L3 experiment. The magnet from this experiment

is also used as part of the ALICE detector, which has been designed to study the

heavy ion physics of the Pb-Pb LHC runs. The last of the big four experiments,

LHCb (Large Hadron Collider beauty experiment) will continue the work of the B-

factories by examining various aspects of flavour physics, notably the measurement

of CP violation in B-meson decays. It is sited at LHC point 8 and uses the pit which

previously held the DELPHI detector. TOTEM is primarily designed to measure

the total LHC pp cross-section in a way that does not depend on the luminosity and

consists of detectors placed each end of CMS at LHC point 5. Finally, LHCf (Large

Hadron Collider forward) is intended to look at the forward region of LHC collisions

26

(very close to the beam pipe) and is located either side of the ATLAS detector.

2.3 The ATLAS Physics Programme

The ATLAS physics programme has an extremely broad coverage by virtue of being

one of the two LHC general purpose detectors. This is covered in detail by vol-

ume II of the ATLAS Detector and Physics Performance Technical Design Report

(TDR) [32] and also in the more recent studies covered in [33]. In summary, the

main physics aims of the ATLAS experiment can be stated as follows:

• Look for the presence of the standard model or other possible Higgs bosons

(such as the MSSM Higgs) in the region between the existing LEP and TeVa-

tron mass limits and the theroretical mass constraint of approximately 1 TeV.

• Carry out searches for supersymmetric (SUSY) particles or other alternative

new physics outside the current Standard Model. It is expected that particle

searches will be possible up to around 5 TeV over the lifetime of the experiment

(limited by the momentum fraction carried by the quarks and glouns which

make up the proton).

• Make precision measurements of the top quark including its mass, decays and

couplings. Studies will cover both tt̄ and single top quark production scenar-

ios. In addition it will be possible to look for the presence of any additional

generations of heavy quarks (requiring associated heavy neutrinos; studies at

27

LEP and SLAC have produced results consistent with there only being three

generations of light neutrinos).

• The electroweak gauge bosons can be examined to produce new precision mea-

surements of the W boson mass, Wγ and WZ production and their associated

Triple Gauge Couplings (TGC).

• A whole array of QCD processes will be studied and precision measurements

made. This will provide both a test of QCD itself, and also allow the back-

ground to other Standard Model (or otherwise) LHC processes to be better

understood.

• There will be a comprehensive B-physics programme to complement that of

LHCb. This will include work on B0s oscillations, CP-violation and measure-

ment of B hadrons including their decays.

• Search for any additional new physics outside the Standard Model (including

the existence of possible new gauge bosons, either charged or neutral).

The ATLAS detector has been designed to perform well with respect to all these

physics areas, in addition to being able to operate successfully in the high luminosity

environment of the LHC, which is required to study them. To do this ATLAS must:

• Have a high radiation resistance and a high detector granularity, coupled to

fast readout electronics, to handle the LHC collision rate.

28

• Be able to work to high values of pseudorapidity (η) and cover the maximum

possible region of azimuthal angle (φ). See 2.4.1.

• Possess excellent ability to identify, resolve and reconstruct charged particles,

plus recognise the presence of secondary vertices (tracking detectors)

• Have electromagnetic calorimetry which allows for good photon and electron

identification and which combined with comprehensive hadronic calorimetry

will allow suitable measurements to be made of transverse jets energies and the

accurate inferring of any missing transverse energy associated with neutrinos.

• Identify muons, including the charge of those possessing high transverse mo-

mentum (pT).

• Be able to trigger on interesting LHC physics processes, including those which

may produce low pT particles, while still rejecting enough background so as to

keep the data rate for final processing and storage within the desired limits.

ATLAS is described in section 2.4.

2.4 ATLAS detector

It is intended to give a general overview of the ATLAS (A Toroidal LHC ApparatuS)

detector, illustrated in Fig.2.4. Further details can be found in the ATLAS Technical

Proposal [34] and the ATLAS Detector and Physics Performance TDR volume I [35],

29

or alternatively through the specific TDR’s corresponding to the various detector

components. To account for specificication changes made during construction, up-

dated information on the key components is contained within the ATLAS Detector

Paper [26].

2.4.1 Detector Overview

As stated previously, ATLAS has been designed to analyse the physics of the LHC

(primarily) pp collisions. Because the LHC beams are symmetric, a cylindrical

geometry was chosen for the detector so as to allow the maximum spatial coverage of

the particles produced in each collision. Furthermore, as a general purpose detector,

it is important that ATLAS is able to measure the properties of all the particles

produced in each event. To do this ATLAS uses a series of different detector layers

arranged radially around the beam pipe.

Different types of particles can be identified by the way they behave in the various

layers. Tracking chambers are usually housed within a magnetic field (this is true for

all the ATLAS trackers) which allows the sign of charged particles to be identified

by observing the direction in which they are bent by the field. The momentum com-

ponent perpendicular to the field can also be determined for charged particles from

the radius of curvature of their tracks. Energy possessed by electrons and photons

is measured by an electromagnetic calorimeter, while a hadronic calorimeter when

combined with the electromagnetic calorimeter provides the energy and position of

hadrons and jets. In addition, the two calorimeters provide information on whether

30

Figure 2.4: The ATLAS Detector [26]

31

any neutrinos or other weakly-interacting particles were present in an event. This is

done by studying whether the total vector sum of the transverse momentum comes

to zero, (as it would be before a collision took place) hence conserving momentum,

or not. If transverse momentum, usually refered to as transverse energy (ET), is not

conserved and some is seen to be ‘missing’ from the calculation, then this imbalance

is assumed to be due to the presence of one or more undetected weakly interacting

particles (such as neutrinos). Conservation of total energy cannot be used as gaps

are required in the detector for the beam pipe and so it is not possible to produce an

accurate measure of the total longitudinal energy in an event (some of the particles

will pass through the gap in the detector if they are produced very close to the beam

pipe). Finally, the muon system (also housed in a magnetic field) provides explicit

muon identification and together with the tracker gives an enhanced measure of

muon momentum. Fig. 2.5 provides a schematic illustration of how these layers

work together to allow the identification of different particle types.

Trackingchamber

Electromagneticcalorimeter

Hadroniccalorimeter

Muonchamber

Innermost Layer ... ... Outermost Layer

muons

±e

, p± π

n

photons

Figure 2.5: Schematic illustration of a slice through a general particle detector

32

ATLAS measures 46 m in length (parallel to the beam pipe), is 22 m in diameter and

weighs 7000 t. Located in the UX15 pit at point 1 of the LHC, the z-axis is taken as

being parallel to the beam pipe and defines the positive direction as towards point

8. The x-y plane is defined as being perpendicular to the beam pipe, with the origin

at the collision point in the centre of the detector. As a right handed co-ordinate

system, the positive x-direction points towards the centre of the LHC ring and the

positive y-direction points vertically upwards. In polar co-ordinates, θ is the angle

from the beam pipe and φ the angle around it. The pseudorapidity (η) is defined in

the usual way 1 [35]. The physical body of the detector can be divided into three

main parts; the inner detector, the calorimeters and the muon spectrometer. These

are discussed here with specific values taken from [26]. In addition there are also

trigger and data aquisition (TDAQ) which will be discussed separately in chapter 3.

2.4.2 Inner Detector

The inner detector consists of a series of different tracking devices mounted inside

a solenoid magnet 5.3 m in length and of 2.46 m inner diameter [26]. This magnet

has been engineered to produce a 2 T nominal field (2.6 T peak field) and has

1The pseudorapidity is defined in terms of the angle θ by η = −ln tan( θ

2) and for particles

travelling close to the speed of light is approximately equal to the particle rapidity (defined in terms

of the particle’s energy and momentum in the direction along the beam axis). Pseudorapidity is

used to define the position of particles in the detector instead of the angle θ because the separation

of particles in η does not depend on the lorentz boost of the particles along the beam axis. This

is not true for θ.

33

also had to be designed so as to minimise the interference produced to particles

travelling through the solenoid and into the surrounding calorimeters. This requires

the amount of material between the tracking detectors and the calorimeters to be

as small as possible. The solenoid shares a vacuum chamber with the liquid argon

(LAr) calorimeter barrel for this reason. As the solenoid produces a magnetic field

parallel to the beam pipe, charged particles are bent in a plane perpendicular to

this. The inner detector itself is 5.5 m long and 2.5 m in diameter and is divided

into a central barrel region 1.6 m long and two matching endcaps [35]. The barrel

consists of a series of cylinders, each consisting of a layer of detectors, wrapped

around the beam pipe (of 36 mm radius). For the endcaps a series of circular disks

are used perpendicular to the beam, with the detectors arranged radially. Both

the barrel and the endcaps contain layers of both silicon and gas filled straw tube

detectors. Fig. 2.6 shows a cut-away view of the complete inner detector, minus the

surrounding solenoid.

Figure 2.6: Cut-away view of the ATLAS inner detector (central solenoid not shown) [26]

34

Three different types of tracking detectors are used in the tracking region. These

are silicon pixel detectors, silicon strip detectors and Transition Radiation Trackers

(TRT) in order of decreasing granularity.

Pixel Detectors

The pixel detectors have the finest granularity of the tracking detectors, each mea-

suring a minimum of 50 × 400 µm. In the barrel region, pixels are arranged in three

layers between radii of 50.5 mm and 122.5 mm (0 is defined as being at the centre

of the beam pipe) and over a length of 802 mm. Each end cap has three disks of

pixels at radii from 89 mm to 150 mm. The two pixel endcaps are found between

495 mm and 650 mm from the collision point at either end of the barrel [26]. In

total there are approximately 140 million pixels.

Strip Detectors (SCT)

Found outside the pixels, the silicon strip detectors are approximately 12 cm long

by 80 µm wide. The barrel has four layers situated between 299 mm and 514 mm

radius and over a length of 1492 mm. Each end cap has 9 disks of between 270 mm

and 560 mm radius and these are situated between 847.5 mm and 2727 mm from

the collision point in each case [26]. Each layer consists of two strip sets, with an

angle of 2.3 degrees between each set. The stereo angle provides a measurement of

z (and thus a value of η) in the barrel, whilst providing a measurement of the radial

distance r in the endcaps. Barrel strips are parallel to the beam pipe and endcap

35

strips arranged radially.

Transition Radiation Tracker (TRT)

TRT are used for the outer layers of the tracking region. Each TRT sensor consists

of a 4 mm diameter tube with a thin wire running down the centre, filled with a gas

mixture (mainly xenon). The barrel straws are 1.44 m long and the end cap straws

0.37 m long [26]. A large potential difference is maintained between the metal tube

walls and the wire so that when a particle passes through a tube, an output signal

is produced which also gives how far from the wire the particle passed (by use of

timing) as well as which tubes were traversed. Although the measurement for a

single tube is not as accurate as that for a single pixel or strip detector, this can be

countered by using many more layers. The TRT barrel has 73 planes of straws set at

radii between 559 mm and 1080 mm over a length of 1430 mm. The end caps have

160 straw planes at radii between 635 mm and 999 mm and in each case between

847.5 mm and 2727 mm from the collision point [26].

In general, the combined tracking region covered by the pixels, SCT and TRT is

|η| < 2.5.

2.4.3 Calorimetry

ATLAS uses a combination of liquid argon (LAr) and tile scintillator calorimeters.

Electromagnetic (EM) calorimetery is provided via a barrel (actually made of two

36

jointed half barrels with a 6 mm gap at the collision point, z = 0) covering |η| <

1.475 and two endcaps covering 1.375< |η| <3.2 [26]. All use LAr technology.

There is also a LAr presampler at |η| < 1.8. Hadronic calorimetery is performed

up to |η| < 4.9 courtesy of a tile scintillator barrel (|η| < 1.0) and extended barrel

(0.8< |η| <1.7), LAr hadronic endcaps (HEC) for 1.5< |η| <3.2 and finally a LAr

forward calorimeter (FCal) for 3.1< |η| <4.9. The complete ATLAS calorimeter

system is shown in Fig. 2.7.

Figure 2.7: Cut-away view showing the complete ATLAS calorimeter [26]

Electromagnetic Calorimeter

Both the EM calorimeter barrels and endcaps use a sampling calorimeter consisting

of layers of lead absorber immersed in LAr to provide the active medium. The lead

absorbers used take an ‘accordion’ shape, intended to give complete, symmetrical,

coverage with respect to φ without the presence of any gaps.

37

The barrel assembly is taken to constitute the two main LAr half barrels and also

the presamplers. As stated in section 2.4.2 the LAr barrel assembly shares a cryostat

with the inner solenoid magnet. This is made from aluminium and insulated via

a vacuum layer. The total length of the cryostat (when the two halves are joined

together) is 6.8 m and the inner and outer radii are 1.15 mm and 2.25 m respectively

[36]. For each EM calorimeter half barrel there are 1024 of the lead accordion

absorbers [26]. The thickness of the lead ranges from 1.53 mm to 2.2 mm on going

from zero to 3.2 in pseudorapidity (η); see [36]. To give structural rigidity, the lead

layers are actually trapped between two sheets of stainless steel 0.2 mm thick. Lead

absorbers, approximately 4 mm apart, alternate with Kapton electrodes required to

read out the calorimeter signals. Presamplers are present in front of the calorimeter

and inside the barrel cryostat in the form of a 1 cm layer of LAr [26], which is read

out by electrodes perpendicular to the beam pipe. In general the barrel is divided

into three sampling layers along its length, while being divided into 32 sectors in φ

to be read out by 7808 channels. There are approximately 110000 channels overall.

A section of the EM calorimeter barrel can be seen in Fig. 2.8, indicating the three

sampling layers. The radiation lengths of the samplings are marked while the accor-

dion shape of the absorbers is also illustrated. For the barrel, the overall material

thickness is > 24 radiation lengths. The finest granularity in the barrel is provided

by the strip layer of the first sampling, so called because of the cell shapes in this re-

gion, which is used to help identify the direction and width of showers (particularly

those produced by photons).

38

∆ϕ = 0.0245

∆η = 0.02537.5mm/8 = 4.69 mm ∆η = 0.0031

∆ϕ=0.0245x4 36.8mmx4 =147.3mm

Trigger Tower

TriggerTower∆ϕ = 0.0982

∆η = 0.1

16X0

4.3X0

2X0

1500

mm

470 m

m

η

ϕ

η = 0

Strip cells in Layer 1

Square cells in Layer 2

1.7X0

Cells in Layer 3 ∆ϕ×�∆η = 0.0245×�0.05

Figure 2.8: A section of the ATLAS EM calorimeter barrel. The three depth samplings

can be seen, together with the accordion shape of the electrodes and the difference in

granularity in the three layers [26]

For each EM calorimeter endcap, eight wedge-shaped units are used to produce

a wheel of 2098 mm radius and 632 mm thickness. Each of these endcap wheels

actually consist of an inner wheel (256 absorber plates) and an outer wheel (768

absorber plates) to cover 2.5-3.2 and 1.375-2.5 in η respectively [26]. The absorber

plates are arranged radially, and are divided into two samplings longitudinally. In

each endcap there is a 5 mm layer of LAr to act as the presampler which is read

out by electrodes parallel to the beam pipe. The endcaps have approximately 64000

read out channels. Each aluminium end cap cryostat has an outer radius (warm

skin) of 2.25 m and a length of 3.17 m. In the endcaps the material thickness is >

24 radiation lengths except for values of |η| <1.475 [26].

Athough both the barrel and endcaps use lead-LAr calorimeters, a large gap is

39

present in coverage at approximately |η| = 1.4 where they meet. To try and reduce

the effect of this for jets, photons and electrons, a slab of scintillating plastic is

positioned in this region. Fig. 2.9 shows a cut-away view of one half of the complete

EM calorimeter system (the hadronic and forward LAr endcaps are also shown but

the gap scintillator is not).

Figure 2.9: Cut-away view showing one half of the ATLAS EM calorimeter (together with

complete endcap)

For both the barrel and endcap the number of calorimeter layers and the granularity

vary as a function of η. Table 2.1 summarises this information for the complete EM

calorimeter [26].

Hadronic Calorimeter

The hadronic calorimeter barrel and extended barrel consists of a tile sampling

calorimeter. The central barrel wraps around the EM calorimeter barrel and has

40

EM Calorimeter Barrel Endcap

Number of layers and |η| coverage

Presampler 1 |η|<1.52 1 1.5<|η|<1.8

Calorimeter 3 |η|<1.35 2 1.375<|η|<1.5

2 1.35<|η|<1.475 3 1.5<|η|<2.5

2 2.5<|η|<3.2

Granularity 4η ×4φ versus |η|

Presampler 0.025×0.1 |η|<1.52 0.025×0.1 1.5 <|η|<1.8

Calorimeter 1st layer 0.025/8×0.1 |η|<1.40 0.050×0.1 1.375<|η|<1.425

0.025×0.025 1.40<|η|<1.475 0.025×0.1 1.425<|η|<1.5

0.025/8×0.1 1.5<|η|<1.8

0.025/6×0.1 1.8 <|η|<2.0

0.025/4×0.1 2.0 <|η|<2.4

0.025×0.1 2.4<|η|<2.5

0.1×0.1 2.5<|η|<3.2

Calorimeter 2nd layer 0.025×0.025 |η|<1.40 0.050×0.025 1.375<|η|<1.425

0.075×0.025 1.40<|η|<1.475 0.025×0.025 1.425<|η|<2.5

0.1×0.1 2.5<|η|<3.2

Calorimeter 3rd layer 0.050×0.025 |η|<1.35 0.050×0.025 1.5<|η|<2.5

Table 2.1: Coverage and granularity of the ATLAS EM calorimeter [26]

41

an inner radius of 2.28 m. The outer radius is 4.25 m and the central section is

5.8 m long, with each of the two extended barrels being 2.6 m in length [26]. Each

tile consists of a steel absorber and a plastic scintillator active medium 3 mm thick.

Layers of tiles are arranged in planes parallel to the beam direction and these are

staggered over depth, making them periodic in z. Wavelength shifting fibres are

used to take the light from both sides of the scintillator for each tile and, running

radially, transfer it to a photomultiplier tube to be read out. By grouping fibres

together it is possible to produce a three dimensional output.

Like the EM calorimeter barrel, the central barrel section is also divided into three

radial layers which provide the three samplings. At η = 0 these layers are designed to

be at radii which give them thicknesses of 1.5, 4.1 and 1.8 interaction lengths respec-

tively [26]. The overall ‘thickness’ of material found inside the ATLAS muon system

(comprising the inner detector and solenoid/cryostat, electromagnetic calorimeter,

hadronic calorimeter and their associated support systems) in total at η = 0 is 11

interaction lengths. This enables hadronic showers/jets to be confined within the

hadronic calorimeter and hence restricts passage of particles other than muons (or

neutrinos) out into the surrounding muon spectrometer [37]. Similarly the two ex-

tended barrels, intended to study the |η| region between 0.8 and 1.7, are also divided

into the same three samplings as the central barrel. Both the central and extended

barrels are divided into 64 sectors with respect to φ, as shown in Fig. 2.10. This

produces an overall granularity of 0.1 × 0.1 in ∆η×∆φ except for in the last radial

layer where it is 0.2 × 0.1 [38].

42

Figure 2.10: Schematic representation of the hadronic tile calorimeter assembly, with a

single module shown for comparison

The two hadronic end-cap calorimeters (HEC’s) use LAr technology similar to the

EM calorimeters, but with a different metal absorber. Intended to cover an |η| range

between 1.5 and 3.2, each end-cap has two wheels of 2.03 m external radius [26].

Both use copper plates as the absorber and LAr as the active medium, with the inner

wheel using 25 mm thick plates and the outer 50 mm thick plates [26]. read out is

provided via the central one of three electrodes found between each set of plates,

which are spaced 8.5 mm apart. A total of 5632 read out channels are present [26].

Both wheels are constructed from 32 units and split into two samplings. The wheels,

which share the end-cap cryostat with the EM calorimeter end-cap and the forward

calorimeter, weigh approximately 67 and 90 tonnes respectively.

Two forward calorimeter (FCal) end-caps, each comprising three module units, are

designed to provide calorimetry in the region 3.1< |η| <4.9 [26], overlapping slightly

43

with the hadronic end-cap calorimeters. The FCal uses a metal matrix and LAr

design, which uses metal rods centred inside metal tubes mounted between two

metal tubeplates. The gaps between the rods and the tubes are filled with the LAr

active medium. Of the three units which make up each FCal, the innermost uses

copper as the metal and contains 12000 tubes and rods, each rod being 4.75 mm

in diameter and the gap between the rod and tube being 0.25 mm [36]. For the

remaining two units, tungsten metal is used. The inner unit has 10000 rods and

tubes with a rod diameter of 4.75 mm and a gap of 0.375 mm, while the outer

unit has 8000 elements, each rod being 5.5 mm in diameter and the LAr gap being

0.5 mm. Both FCals are read out by 11288 channels. The design of the FCal was

formulated largely to try to limit the damage produced by the high particle flux that

will be present in the FCal region. For this reason, a copper ‘plug’ is also located

behind each of the FCals to attempt to protect the forward muon chambers of the

detector. Fig. 2.11 illustrated the general layout of the FCal.

Figure 2.11: General arrangement of the LAr forward calorimeter

44

2.4.4 Muon Spectrometer

The muon spectrometer is what defines the overall size of the ATLAS detector. It

consists of three superconducting air-cooled toroid magnet systems, one barrel and

two endcaps. These magnets are used to bend the path travelled by muons, which

is recorded by a series of tracking chambers in both the barrel and endcap regions,

as per the inner detector.

All three of the toroid magnets use eight coils arranged around the beam axis. In

the barrel, each coil that makes up the toroid is approximately 25 m long, 5 m

wide and weighs 40 tonnes. They are comprised of two double-pancake windings

of 20.5 kA NbTi superconducting wire, stabilised using aluminium [35], and are

contained inside an alloy outer shell. In addition, all the barrel coils have individual

cryostats to provide the cooling, weighing 40 tonnes each, which are used as part

of the structural support for the whole toroid, together with additional alloy struts.

The eight coils are linked together and mounted on the detector feet as shown in

Fig. 2.12 to produce a toroid with inner and outer diameters of 9.4 m and 20.1 m

respectively [26]. The barrel toroid produces a peak field of 3.9 T and in the region

for |η| of 0.0-1.4 the bending power produced is from 2 to 6 Tm.

The two end-cap toroid magnets use the same coil winding type as for the barrel,

with each of the eight coils per endcap measuring approximately 4.5 × 4 m and

weighing 13 tonnes. The smaller size means that for each end-cap the eight coils

are mounted into one single structure housed in a single cryostat. Each assembled

magnet has an inner diameter of 1.65 m and an outer diameter of 10.7 m [26];

45

Figure 2.12: Illustration of how the eight coils of the ATLAS barrel toroid magnet are

linked together and mounted on the detector feet

the complete assembly including the cryostat is approximately 5 m long, 11 m in

diameter and weighs roughly 240 tonnes. A complete endcap unit is illustrated in

Fig 2.13. The peak field for each end-cap toroid magnet is 4.1 T and the resultant

bending power is 1 to 8 Tm for |η| from 1.6 to 2.7. Each end-cap toroid is mounted

within the relevant end of the main barrel toroid. To permit this and to maximise

the bending power possible in the region 1.4< |η| <1.6 where overlap of the two sets

of fields occurs, the coils of the barrel and end-cap are offset relative to each other

by 22.5◦ in φ. Despite this, the bending power is still reduced in this region.

Measurement of muons in the spectrometer is carried out using four different types

of tracking detectors. As with the other detector components, these are arranged

into a barrel region and two sets of big wheel end-caps. The barrel provides coverage

for |η| <1 and comprises three layers of chambers, wrapped around the beam pipe,

46

Figure 2.13: View of one of the ATLAS end-cap toroid magnets

at 5, 7.5 and 10 m radius [26]. End-cap coverage is for 1.0< |η| <2.7, with each

end-cap having four big wheels of radially arranged chambers located perpendicular

to the beam pipe at distances of 7.4 m, 10.8 m, 14 and 21-23 m from the collision

point at the centre of the detector [26]. The spacing of the layers of muon chambers

is shown in Fig. 2.14

Precision position measurement of the muon primary coordinates (in the main mag-

net bending plane) is mainly provided by 11088 Monitored Drift Tubes (MDTs)

for |η| <2.7, with 32 Cathode Strip Chambers (CSCs) replacing the inner endcap

layer of MDTs for 2.0< |η| <2.7 [26]. These are read out by 339000 and 30700

channels respectively [26]. Measurement of the secondary muon coordinate (in the

non-bending plane and perpendicular to the primary) and also triggering is provided

via 544 Resistive Plate Chambers (RPCs) for |η| <1.05 and 3588 ThinGap Cham-

bers (TGCs) for 1.05< |η| <2.4 [26]. Triggering is not provided for |η| >2.4. These

47

Figure 2.14: Section throught the side of the ATLAS detector illustrating the arrangement

of the muon chambers [26]

chambers are read out by 359000 channels for the RPCs and 318000 channels for

the TGCs [26]. The location of the different chamber types is summarised in Fig.

2.15.

2.5 ATLAS analysis tools

Within the ATLAS experiment a standard framework exists for use in all ATLAS

physics analysis. This Athena framework is primarily designed to carry out analysis

on Analysis Object Data (AOD) files which are the format in which the majority

of the real data from the running ATLAS experiment are stored. Athena uses

algorithms written in C++, controlled by job option files written in python, to

carry out the desired analyses.

48

Figure 2.15: Location of the different chamber types within the muon spectrometer

49

To compare the real ATLAS data to theory and to evaluate different analysis strate-

gies, it is necessary to produce artificially sets of AOD files for a whole series of dif-

ferent processes. These ‘Monte Carlo’ datasets are produced by a process referred

to as running the ATLAS full chain, illustrated in Fig. 2.16.

Figure 2.16: Flow diagram showing the stages required to produce artificially ATLAS

AOD datasets

Events are produced by an ATLAS approved generator 2, such as MC@NLO [39],

Pythia [40] or Herwig [41], and passed through a full simulation of the ATLAS de-

2An event generator simulates the various stages of a particle collision. It reproduces the initial

state and any associated radiation, the hard scatter, and the production and then subsequent decay

of particles in a given physics process. Final state showering and radiation are also produced.

Generators can be tuned depending on the particular process and conditions being studied

50

tector provided by GEANT4 [42]. Simulated detector hits (recording which sensors

within ATLAS fired for a given event, together with the size of the recorded sig-

nals) are converted into raw data objects (RDO) by the digitization stage. For real

ATLAS data the raw output of the readout (‘bytestream’) is unpacked into RDO

format as the first stage of the reconstruction. The same process is now followed

for simulated and real ATLAS data. RDO undergo an event reconstruction stage

to produce Event Summary Data (ESD) files, which are a detailed output format.

These are then condensed to produce finally the AOD files for analysis. AOD consist

of collections which contain the information relating to the different particle types;

for example the electron collection contains information on the η, φ, pT and so on

of each electron recorded in the event, together with a summary of any quality cuts

applied. In addition to the various reconstructed particle types, there are separate

collections for jets, trigger information, truth information (for simulated data only)

and selected information on tracks, calorimeter clusters and similar. Truth infor-

mation contains the details about an event as produced by the generator before the

detector simulation was applied.

2.6 Conclusions

An overview of the Large Hadron Collider at CERN has been presented. The main

components of the accelerator complex have been briefly described, together with

how they are used to produce proton-proton collisions at a given centre of mass en-

ergy. Figures were provided for the design beam parameters and also those used to

51

collect a total of 46 pb−1 of proton-proton collision data (for a centre of mass energy

of 7 TeV) during 2010. The ATLAS experiment was introduced and the ATLAS

physics programme was briefly covered, together with the resulting detector require-

ments. An overview was given of the complete ATLAS detector and how it is used

to identify different experimental signatures. A detailed description was provided of

the various ATLAS subdetectors, focusing in particular on the electromagnetic and

hadronic calorimeters, while finally the ATLAS data format and analysis framework

was summarised.

52

Chapter 3

The ATLAS Trigger System

3.1 Introduction

Within this chapter is provided an overview of the ATLAS trigger system. The three

trigger levels are introduced and briefly described. Further detail is then provided

on the first level calorimeter trigger, describing how regions of interest are formed

and how the trigger menu thresholds are assigned.

3.2 ATLAS Trigger Overview

The ATLAS trigger system is designed to reduce the ATLAS data rate sufficiently

that permanent storage is possible. In doing so, it must retain as far as is possible

the maximum number of ATLAS events which are likely to yield new physics or are

53

required for detailed study, while at the same time discarding those events which

are of minimal interest. When the LHC is running at the design luminosity of

1034 cm−2s−1 the bunch crossing rate of 40 MHz produced will correspond to a pp

interaction rate of approximately 1 GHz. This had to be reduced in the 2009-2010

running to just 200 Hz for storage on disk [43]. From 2011 storage of the complete

ESD (see 2.5) was to be dropped for most events, allowing the final data rate to be

raised to 400 Hz. The final rate is limited by the amount of data storage available,

together with the time required to analyse the data fully. In general, this is mainly

done by removal of the low pT QCD events produced by soft pp collisions.

The ATLAS trigger uses three levels. Level 1 is hardware based and reduces the

∼1 GHz LHC interaction rate to 75 kHz. A maximum of 2.5 µs is available for the

level 1 trigger decision, however a 2.2 µs latency is actually used for caution. The

rate is then further reduced by the software based level 2 to ∼3.5 kHz, which takes

approximately 40 ms (on average) [43]. Finally the Event Filter (EF) is applied

to reduce the overall rate to a few hundred hertz ready for storage on hard disk.

The difference between level 2 and the event filter is described in 3.3.2 and 3.3.3.

Approximately 4 s is required for the Event Filter stage, which is able to use offline

algorithms as part of the selection process. Level 2 and the Event Filter are jointly

referred to as the higher level trigger (HLT). The three trigger levels are summarised

in Fig. 3.1.

54

LEVEL 2TRIGGER

LEVEL 1TRIGGER

CALO MUON TRACKING

Event builder

Pipelinememories

Derandomizers

Readout buffers(ROBs)

EVENT FILTER

Bunch crossingrate 40 MHz

< 75 (100) kHz

~ 3.5 kHz

~ 200 Hz

Interaction rate~1 GHz

Regions of Interest Readout drivers(RODs)

Full-event buffersand

processor sub-farms

Data recording

Figure 3.1: Overview of the ATLAS trigger system [43]

3.3 Trigger Performance

3.3.1 Level 1 Trigger

At level 1 (LVL1), the speed of response required means that the whole ATLAS

detector is not read out. Instead, the LVL1 trigger decision is made by accessing

only the calorimeters and muon detectors. In addition, the granularity used at LVL1

from these systems is coarser than what is actually possible for these two subsystems.

For the calorimeters, reduced granularity is used in both the barrel and endcaps for

both EM and hadronic parts. For the muon detectors, only the trigger RPCs and

TGCs are used in the barrel and endcaps respectively (see sections 2.4.3 and 2.4.4

for details of the calorimeters and muon spectrometer). While the LVL1 decision is

awaited, events are stored in the on detector pipeline memories. For those bunch

crossings which pass LVL1 this is then read out from the detector and passed on

55

to storage in the readout buffers (ROBs). Events not selected are discarded and

cannot be recovered. The Central Trigger Processor (CTP) is responsible for using

the LVL1 muon and LVL1 calorimeter data to produce the decision, based upon a

trigger menu of various different items [43]. LVL1 muon and calorimeter triggers

together look for [44]:

• High pT muons

• High pT electrons and photons

• Jets and taus decaying to hadrons

• Large missing and total ET

The LVL1 trigger has two main purposes. The first is to deduce whether a particular

LHC bunch crossing is likely to contain an event which may be of interest for further

study, and hence whether the corresponding information should be retained and

passed to the level 2 (LVL2) trigger or not. Secondly, if an event is noted as being

of interest at LVL1, the LVL1 trigger also produces Regions-of-Interest (RoI), in

terms of η and φ coordinates, that mark the areas of the event which are of interest.

It is these areas that are studied by LVL2 in order to make the LVL2 decision.

Information on the trigger thresholds passed at LVL1 is also available.

56

3.3.2 Level 2 Trigger

At LVL2 the full granularity information is available for the calorimeters and muon

chambers, plus the inner detector is also used, again at full granularity. However, the

LVL2 trigger is only allowed to use data from the regions which have been marked by

a LVL1 RoI. By restricting the fraction of the detector read out available to LVL2,

the bandwidth and processing requirements needed are reduced. This is done by

the LVL2 trigger using the RoI information as a guide, so as to look only at the

specific parts of the data in the ROBs necessary to make the LVL2 decision. LVL1

produces two types of RoI, both of which can be studied by LVL2. Primary RoI

are those produced by signatures within an event which were directly responsible

for the event passing LVL1. Secondary RoI are produced for features of interest

that were not directly responsible for the event selection (these are little used at

present). By use of the RoI system, the amount of data which has to be processed

at LVL2 before a decision is made is approximately 2% of the total readout [43],

and as a result the trigger latency is reduced accordingly. Events which pass the

LVL2 trigger condition are moved from the ROBs on to the Event Filter via the

event building stage. Event building results in all the data for a particular event

being stored as one item, rather than being split up as at earlier trigger stages. As

for LVL1, events which are not selected by LVL2 are discarded completely.

57

3.3.3 Event Filter

The Event Filter (EF) uses sophisticated algorithms, of the type normally used for

offline analysis, which have been adapted to work online and provide the final stage

of event rejection. Use of conventional offline algorithms that have been packaged

up to work online removes the need to develop software specifically tailored to the

EF. Unlike LVL1 and LVL2, the EF has the ability to use all the data for each event

which are received via the event builder. However, the EF algorithms are expected

to be ‘seeded’ on what areas of the data to concentrate on by the results of LVL2.

In order to realise the desired data rate of 200 Hz for hard disk storage, the EF is

expected to [45]:

• Reject any remaining events which are not desired for physics analysis

• Minimise storage size (if possible) for events which pass the EF

• Apply some data compression

For initial ATLAS running, LVL2 and the EF were switched off. Here, events

successfully selected by LVL1 effectively passed straight through the HLT and on to

permanent disk storage. The HLT was enabled when necessary during 2010, with

the selection applied depending on which signatures were needed and validated at a

given time. The EF will play an increasingly important role as the LHC luminosity

is ramped up.

58

3.3.4 Trigger Menus, Chains and Event Selection

The ATLAS trigger decision for a given event is made by referencing a set trigger

menu stored in a database. The menu comprises a large number of items, each of

which has a particular signature for the three trigger levels. Each item comprises a

chain of signatures with the LVL2 signature building on from the LVL1 thresholds

and likewise the EF signature refining that of LVL2. For a given event, the LVL1

trigger signatures are first checked for each chain. Should all chains fail at this stage

then the event is immediately rejected. Otherwise, the remaining chains progress to

LVL2 where the process is repeated. If any of the chains pass all three levels, then

the event is accepted and written to storage on disk.

ATLAS trigger menus also allow for prescaling of the items. Prescales are fac-

tors which can be applied to a given trigger signature to ensure that only a pre-

determined fraction of the events that would otherwise have passed the signature

can do so. As a consequence, they allow the trigger to select lower priority but still

interesting physics events without compromising the overall trigger rate. All three

levels of the trigger have the capability for prescaling and a given trigger chain can

contain a mixture of prescaled and non-prescaled signatures.

59

3.4 Level 1 Calorimeter Trigger

3.4.1 Overview

As described in 3.3.1 the level 1 calorimeter (L1Calo) trigger uses a reduced gran-

ularity from the ATLAS calorimeters. This granularity varies depending on the

trigger being considered.

3.4.2 Cluster Triggers

For electron/photon and tau/hadron cluster triggers, the granularity used is ap-

proximately 0.1×0.1 in 4η ×4φ 1 and the calorimeter elements are arranged into

approximately 7200 trigger towers [43], which split into electromagnetic (EM) trig-

ger towers and hadronic trigger towers. L1Calo cluster triggers only cover |η| <2.5,

the region corresponding to inner tracker and high granularity calorimetry coverage

[46]. The details of how the L1Calo electronics are arranged have been described

in a number of sources, such as [26], and will not be discussed here. The trigger

towers are grouped into EM and hadronic clusters, cores and isolation rings and are

analysed by an algorithm which uses a sliding 4×4 trigger tower window as shown

in Fig. 3.2 [46].

EM clusters are formed by summing pairs of adjacent trigger towers in the 2×2 EM

core, in the centre of the algorithm window, over the depth of the EM calorime-

1Actual granularity used is 0.1× π

32in 4η ×4φ

60

Figure 3.2: Groupings of trigger towers used in L1Calo electron/photon and tau/hadron

triggers [43]

ter. The equivalent 2×2 tower block, located behind the EM core, in the hadronic

calorimeter is defined as the hadronic core. Hadronic clusters are also formed by

summing each of EM clusters, with the hadronic core. The transverse energies de-

posited in these regions (the ATLAS trigger works entirely in ET) are defined as

being the EM cluster energy, EM core energy, hadronic (or tau) cluster energy and

the hadronic core energy. In addition, the 12 towers around the EM core are defined

as the EM isolation ring, and the equivalent 12 towers in the hadronic calorimeter

around the hadronic core are defined as being the hadronic isolation ring. The en-

ergies deposited in these rings are defined as being the EM isolation and hadronic

isolation energies respectively. It is by setting limits on the amount of energy allowed

in these different regions that the trigger isolation thresholds are defined.

61

Electron/Photon Trigger

The electron/photon and hadron/tau triggers together have a total of 16 different

sets of programmable thresholds. Eight of these are allocated to the electron/photon

trigger only, with the remaining eight shared between the two triggers as desired.

The electron/photon thresholds use cuts on the EM cluster energy and on three

different isolation energies (EM isolation ring, hadronic isolation ring and hadronic

core) to select candidates. To pass the electron/photon trigger, the most energetic

EM cluster must have an energy larger than the EM cluster threshold and the three

isolation sums produced must be less than or equal to the appropriate thresholds.

Hadron/Tau Trigger

A maximum of eight threshold combinations exist for the hadron/tau trigger. The

thresholds are on the hadron/tau cluster energy plus the EM and hadronic ring

isolation energies. The most energetic hadron/tau cluster must have an energy

larger than the hadronic cluster threshold and the EM and hadronic isolation ring

energy sums must be less than or equal to their associated thresholds for a particular

hadron/tau trigger to be passed.

In addition to the cluster and isolation conditions, a window can only produce an

RoI if the central 2×2 ‘core’ cluster (EM plus hadronic) is an ET maximum when

compared to the eight other ‘cores’ of the surrounding, overlapping windows. The

requirement avoids multiple counting of, for example, a large energy deposit centred

62

in only one or two trigger towers [43]. The cluster RoI consists of the EM core (2×2

cluster region) added to the hadronic core. Successful cluster trigger candidate RoI

are passed on to the LVL2 trigger, together with details of which trigger thresholds

have been passed.

3.4.3 Jet Trigger

The L1Calo jet trigger covers the region |η| <3.2 and uses a lower granularity than

the cluster triggers. Instead of just using trigger towers alone, the jet trigger uses

jet elements consisting of blocks of 2 × 2 towers and as a result each element has a

granularity of approximately 0.2×0.2 in 4η×4φ. A jet trigger RoI consists of 2×2

jet elements summed over the depth of the EM and hadronic calorimeters. Jet ET

can be measured via one of three different algorithm windows, and these are shown

in Fig. 3.3.

Figure 3.3: Groupings of jet elements used in the L1Calo main jet trigger for jet ET

measurement (Jet RoI are hatched) [43]

There are eight threshold groups for the jet trigger, each of which comprises a

particular choice of algorithm window size and a value for the minimum jet ET. If

63

the jet trigger is passed, a jet trigger candidate is produced. For this to happen, the

ET of the jet window must exceed the minimum jet ET threshold and the ET of the

jet RoI must be larger than that of the surrounding RoI. The jet trigger candidates

produced are passed on to LVL2.

In addition to the main jet trigger, there is also an ATLAS forward jet trigger that

covers |η| <4.9. This makes use of the ATLAS forward calorimeters and has four

threshold groups. The granularity is also further reduced relative to the main jet

trigger.

3.4.4 Missing ET and Total ET Triggers

The missing and total ET triggers use the full calorimeter system, including the

forward calorimeters, and hence cover the region |η| <4.9. A summation over jet

elements (as used for the jet trigger) is carried out to produce a map of the energy

coverage which has a granularity of 0.2×0.2 in 4η × 4φ. The Ex and Ey vectors

are summed to produce a vector corresponding to the direction of any missing ET

present in the event. All the ET values recorded in the calorimeter are also simply

added to produce a value for the total event scalar ET. For details on how Ex and

Ey are obtained in the trigger hardware, see [46]. The missing ET trigger has eight

thresholds while in 2009-2010 the total scalar ET trigger had four thresholds. From

the 2011 run the total ET trigger will also have eight thresholds, and a new trigger

on missing ET significance, proportional to missing ET/√

(SumET), will be added.

64

3.5 Conclusions

An overview was provided of the ATLAS trigger system. The three trigger levels

were introduced, comprising the hardware based level 1 and the software based level

2 and event filter (together known as the higher level trigger), and each briefly

described. This was followed by a note on how the levels are combined into trigger

chains and menus. Finally, more detail was provided on the level 1 calorimeter

trigger including information on how the cluster, jet and and missing/total ET

triggers are formed.

65

Chapter 4

Level 1 Tau Trigger Performance

4.1 Introduction

Contained within this chapter is a description of a study carried out into the per-

formance of the ATLAS level 1 tau trigger. Official ATLAS simulated data were

used for samples of tt̄ and Z → ττ events to make comparisons between the Monte

Carlo truth taus present and the Regions of Interest (RoI, see chapter 3 for details)

produced when the generated events were passed through a complete simulation of

the ATLAS detector and trigger system. The aim of the study was to look at the

level 1 tau trigger performance for different processes, trigger thresholds, isolation

cuts and over a range of pT. Z → ττ events provided a very clean source of taus

which in principle are easy to trigger on, whereas tt̄ events tested the trigger in a

much more complicated enviroment, but one which is normal at the LHC.

66

4.2 Trigger analysis details

The work detailed in this chapter was initially carried out in Athena release 11.0.41/12.0.6

for a centre of mass energy of 14 TeV prior to the commencement of LHC running.

This was carried out as part of the ATLAS ‘CSC’ (Computer System Commission-

ing) effort which was a collaboration wide exercise to test the readiness of all analyses

prior to the planned start of data taking. The precise details covered here began as

an examination of the acceptance of a proposed tau trigger menu for top physics,

which was extended to examine the performance of LVL1 tau trigger isolation as a

function of pT and cluster cut value. As the LHC beam energy changed between the

end of the CSC effort and the beginning of data taking in 2010, these studies were

subsequently revisited in 2010 when a more realistic set of trigger simulations were

available. Also presented in this chapter are the results of repeating this analysis

for release 15.6.13.7 7 TeV centre of mass simulated data. Differences produced as a

result of the centre of mass energy change, together with changes made to the trig-

ger calibration between the two releases, are stated where necessary. Analysis was

carried out on complete sets of AOD files without the application of any preselection.

To produce the results described, datasets of two event types were considered, all of

which were produced centrally by ATLAS. The first was the tt̄ dataset containing

semileptonic and dileptonic decaying tt̄ events, with leptonic decays of top quarks

to taus allowed to occur. The second was the Z → ττ sample. For release 12.0.6

the 14 TeV tt̄1 and Z → ττ 2 samples used formed part of the ‘CSC’ production.

1Sample trig1 misal1 mc12.005200.T1 McAtNlo Jimmy.recon.AOD.v12000604 tid0079002Sample trig1 misal1 csc11 V2.005188.A3 Ztautau filter.recon.AOD.v12000601 tid008566

67

The equivalent 7 TeV tt̄3 and Z → ττ 4 samples used in release 15.6.13.7 were taken

from the ‘mc09’ production.

Within ATLAS data (for real and to a lesser extent simulated samples) the LVL1

trigger information can be accessed in a number of different ways. For this study

the LVL1 trigger objects within the AOD were used. Details were obtained of LVL1

RoI produced by anything passing the LVL1 EM or tau cluster triggers in an event

5. These included the η and φ values of each RoI produced, plus the values of

the various core, cluster and isolation energies (for further details on how these are

defined, see 3.4.2 ). Also used was the ‘Monte Carlo’ truth information for the

events, namely the values for η, φ and pT of each truth particle. Information on the

parents and daughters of each truth particle was also used to compute the visible

pT of the truth taus as described in 4.4.1.

4.3 Truth matching of taus

The analysis used spatial matching between each truth tau particle in each event

and its associated RoI should one be present. Whenever a tau was found in the

truth particles, an algorithm would loop through the relevant RoI’s for the event

and compare each to the truth tau, calculating the separations 4η and 4φ between

3Sample mc08.105200.T1 McAtNlo Jimmy.merge.AOD.e357 s462 r635 t534Sample mc08.106052.PythiaZtautau.merge.AOD.e347 s462 r635 t535At the time of the CSC studies, information on LVL1 RoI was to be found, in differing formats,

inside two separate objects within the software. These were merged into a single object by the

time the later data were analysed

68

the truth particle and each RoI. The 4R in each case was thereby calculated using

4.1.

4R =√

(4η2 + 4φ2) (4.1)

For each truth tau the best matching RoI was assigned as giving the smallest 4R.

Fig. 4.1 shows the minimum | 4R| values corresponding to the closest RoI for each

truth tau, inside the region |η| <2.5 covered by the L1Calo cluster trigger.

R∆Min. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Even

ts10

log

1

10

210

310ττ→Z

tt

Figure 4.1: Minimum |4R| corresponding to the best matched RoI plotted on a log scale

for both tt̄ and Z → τ τ events (14 TeV centre of mass energy)

The difference in environment present for the tt̄ and Z → τ τ events can be seen

in Fig. 4.1. For Z → τ τ events, the τ+ and τ− should generally be produced back

to back in φ. Thus a peak corresponding to the mismatched taus in the Z → τ

τ plot occurs at 4R ≈ π. For tt̄ events containing one or more taus there are a

number of other items present in each event which could produce an RoI. Hence the

tt̄ distribution over 4R is continuous for the poorly matched taus rather than being

peaked as for Z → τ τ .

69

4.4 Tau Trigger Efficiencies

The LVL1 tau trigger efficiency was examined in a variety of senarios. A value of

4R = 0.3 was used to determine whether the trigger had fired correctly or not.

Truth taus less than 4R = 0.3 away from the closest RoI were referred to as being

well spatially matched to an RoI and considered a trigger success. For truth taus

with 4R > 0.3, the trigger was considered to have failed. The tau cluster threshold,

EM isolation threshold and hadronic isolation thresholds were varied, while the EM

cluster threshold was not used. Only taus within the real calorimeter coverage of

|η| < 2.5 were considered.

Due to the complex nature of tt̄ events, taus can be produced in different ways. It is

considered important to trigger with high efficiency those taus which come directly

from the W-boson produced by the decay of the top (referred to here-on as ‘prompt

taus’). For the top sample used, such taus comprised ∼82% of the truth taus in

the range |η| < 2.5, as opposed to those from other sources such as B-mesons.

Consequently, all aspects of the analysis were carried out initially for just those

prompt taus coming from the W from the top and then for all taus within the tt̄

sample.

4.4.1 Efficiency without application of isolation

Initially the trigger efficiency, plotted versus the truth tau visible pT, was considered

without any isolation conditions being applied.

70

The truth visible pT represents what the trigger should see in an ideal calorimeter

with an ideal cluster. It was calculated by taking the truth tau pT and subtracting

from it the pT associated with any muons or neutrinos which are daughter particles

of the decaying tau. This was done component by component with the ‘visible pT’

being reconstructed at the end of the process. In all the samples used, truth taus

can be seen to radiate one or more photons before actually decaying. The pT of the

tau was taken at the point where it decayed into daughters.

A series of different tau cluster thresholds was applied to the samples with values

chosen to resemble an ATLAS LVL1 early trigger menu. Values of 5, 6, 9, 11, 16, 25

and 40 GeV were applied. Fig. 4.2 shows the efficiency as a function of the visible

pT for the prompt taus in the 14 TeV and 7 TeV tt̄ samples and for a tau cluster

threshold of 25 GeV. In Fig. 4.3 the efficiency is shown versus the visible pT for four

of the tau cluster thresholds, again for the prompt taus in the 14 TeV tt̄ sample.

Fig. 4.4 shows the equivalent plots for the 7 TeV tt̄ sample.

From Fig. 4.2(a) it can be seen that before isolation cuts are applied the trigger

performance appears satisfactory with full efficiency being reached for a truth visible

pT value of approximately 30 GeV and an efficiency at threshold of approximately

98%. The turn on is not as sharp as would be expected for an equivalent electron or

muon trigger. Fig. 4.3 illustrates this with the turn on curves for the four thresholds

overlapping despite comparatively large threshold spacings. Looking at Fig. 4.2(b)

it can be seen that for the 7 TeV tt̄ sample full efficiency is reached at approximately

the same value of the tau visible pT as for the 14 TeV sample, but with a softer

71

[MeV]T

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(b) 7 TeV

Figure 4.2: Trigger efficiency as a function of the truth visible pT for a tau cluster threshold

of 25 GeV. The turn on curve is for prompt taus in tt̄ events. No isolation condition is

applied

[MeV]TTrue Visible Tau p0 10000 20000 30000 40000 50000 60000

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Figure 4.3: Trigger efficiency as a function of the truth visible pT for four tau cluster

thresholds. The turn on curves are for prompt taus in tt̄ events. No isolation condition is

applied (14 TeV centre of mass energy)

72


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Figure 4.4: Trigger efficiency as a function of the truth visible pT for four tau cluster

thresholds. The turn on curves are for prompt taus in tt̄ events. No isolation condition is

applied (7 TeV centre of mass energy)

turn on for the same tau cluster threshold of 25 GeV. The efficiency at threshold

is fractionally smaller for the 7 TeV sample, at approximately 95%. Comparing

Fig. 4.3 and Fig. 4.4 it can be seen that this behaviour is common across all four

thresholds, with the turn on being softer for the 7 TeV sample in each case but with

maximum efficiency reached for approximately the same value of the truth visible

pT of the tau.

The difference observed between the 14 TeV and 7 TeV results is largely due to

changes made, in the simulated L1Calo trigger calibration and tower noise cuts,

between the production of the 14 TeV and 7 TeV samples. In the 14 TeV samples,

settings had been used which were intended to represent a finalised tuning of the

trigger. The ET calibrations of the trigger towers had been adjusted (by varying the

73

gains), to partially compensate for the varying amounts of material located in front

of the calorimeter (dead material correction). This served to provide as uniform a

response (i.e. trigger turn on) as possible as a function of trigger tower η. Gain

levels were also set so as to improve the hadronic response in relatively energetic

jets, with tower noise cuts kept low to increase sensitivity to small signals. A more

realistic trigger configuration was applied for the 7 TeV Monte Carlo production,

so as to better describe the detector performance observed during the commission-

ing of ATLAS. Trigger towers were calibrated by simply matching the ET seen in

each tower to the raw ET measured for the corresponding cells in the readout. This

‘EM scale’ calibration does not correct for the variation in dead material in front

of the calorimeter, resulting in slightly lower signals and the trigger efficiency turn

on developing a less uniform η dependence (softer where more material is present).

When averaged across the whole calorimeter, the overall trigger turn on produced

was therefore less sharp than for the older idealised calibration. Furthermore, to

match the commissioning data, higher electronic noise threshold cuts and less uni-

form pedestal subtractions were applied to trigger towers in the 7 TeV samples. All

these factors reduce the sensitivity of the trigger to small signals, compared to the

14 TeV Monte Carlo, and so produce a slower turn on for a given trigger threshold.

A check was carried out on the process dependence of the LVL1 tau trigger before

the application of any isolation constraints. In Fig. 4.5 the efficiency versus visible

tau pT is shown for both tt̄ events and Z → τ τ samples for the 25 GeV tau cluster

threshold. No clear process dependence is apparent as a function of the tau visible

pT.

74

[MeV]T

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Effic

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ττ→Z

tt

Figure 4.5: Trigger efficiency as a function of the truth visible pT for a 25 GeV tau cluster

threshold. The turn on curve is shown for tt̄ and Z → τ τ events. No isolation is applied

and only prompt taus are included for tt̄ events (14 TeV centre of mass energy)

A further comparison was made between the turn on curves for the top sample

when considering only the prompt taus, to the turn on curves when all the truth

taus were used. Comparison between the two cases as a function of the visible pT of

the tau is presented in Fig. 4.6 where no isolation was applied. What is observed for

both 14 TeV and 7 TeV centre of mass energies is a softening of the turn on curve

when all the taus in the sample are included instead of just the prompt taus. The

efficiency turn on also occurs earlier when all taus are considered, with the efficiency

in each bin being larger than for the prompt taus until the plateau is reached. This

is explained by the fact that the efficiency is plotted as a function of the visible pT

of the truth tau. For the prompt case the tau is produced as an isolated object and

so the energy seen by the L1 tau cluster is largely due to tau alone. When all the

75

taus are taken into account, 20% of the truth taus originate from a B-meson and

so would be expected to lie either inside, or in close proximity to, a particle jet. If

an isolation constraint is not applied, then in the latter case the energy recorded

by the L1 tau cluster would include energy from the jet, as opposed to just the

tau visible energy. Consequently, taus located within a jet can pass the L1 trigger

despite having an energy below the tau threshold, whereas prompt taus cannot.

Therefore when the trigger efficiency is plotted as a function of the true visible tau

pT the turn on is softer than is seen for the prompt taus alone. As the probability

of correctly reconstructing a tau produced from B-meson decay is close to zero, for

physics purposes it is the performance of the trigger for the prompt taus that is

important.

[MeV]T

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Figure 4.6: Trigger efficiency as a function of the truth visible pT for a tau cluster threshold

of 25 GeV. The turn on curve is shown for both the prompt taus alone and for all the taus

in the tt̄ sample. No isolation condition is applied

76

4.4.2 Effect of different isolation cuts

The effect of applying a series of EM and hadronic isolation cuts on the trigger

efficiency was studied as a function of the truth visible pT of the tau. The same

trigger condition and constraints, as discussed in 4.4.1, were retained with a fixed

tau cluster threshold of 25 GeV also being added. A series of new cuts were then

applied on the energy allowed in the RoI EM and hadronic isolation rings (defined

in Fig. 3.2). Cuts were applied separately for the EM and hadronic isolation cases.

Refinement of the cuts was carried out in order to focus on the region sensitive to

changes in the size of the isolation cut6. The final values chosen were:

• EM isolation cuts of 4, 5, 6, 7 and 8 GeV

• Hadronic isolation cuts of 2, 3, 4, 5 and 6 GeV

Results for 14 TeV centre of mass energy

It was seen for a centre of mass energy of 14 TeV that the smaller cuts produced

too drastic an effect on the efficiency, but that the larger cuts offered the potential

to be used to improve the rejection against fake taus. Fig. 4.7 demonstrates this by

showing the results of applying 4 and 6 GeV EM isolation cuts and 2 and 5 GeV

hadronic isolation cuts on the trigger efficiencies for the prompt taus in the tt̄ sample

respectively.

The cuts on the isolation were studied for a fixed cut on the tau cluster pT of

6Optimised for the 14TeV sample

77

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(b)

Figure 4.7: Plots of tau trigger efficiency versus truth visible pT, with isolation applied,

for prompt taus in the tt̄ process for a centre of mass energy of 14 TeV. The left plot shows

the effects of 4 and 6 GeV cuts on EM isolation while the right plot shows the effect of 2

and 5 GeV cuts on hadronic isolation

25 GeV. Fig. 4.7 shows how the isolation cuts affect the trigger efficiency as pT

increases. Above approximately 30 GeV, as the truth visible pT of the tau increases

there is a drop off in the efficiency observed. Tightening the isolation cut causes a

more dramatic fall off in efficiency. This occurs because as the tau pT increases, so

the level of leakage into the isolation rings increases and more events become liable

to fail the isolation condition. In Fig. 4.7 the 4 GeV EM isolation cut and the 2 GeV

hadronic isolation cut produced a very dramatic drop in the efficiency above around

40 GeV. By contrast, the 6 GeV EM isolation cut and the 5 GeV hadronic isolation

cut have an effect that is much less dramatic for both samples. These isolation

cuts do not particularly damage the trigger efficiency up to around 80 GeV. Thus

isolation cuts of this magnitude should be useable to reduce the number of events

being triggered by fake taus for a collision centre of mass energy of 14 TeV.

78

The fall off in efficiency observed for values of the tau visible pT notably larger

than the cluster threshold means that care must be taken when tuning LVL1 tau

trigger menus. It is important to ensure the changeover from one isolated threshold

to the next occurs before the lower threshold trigger efficiency starts to fall away

from the plateau level. Furthermore, the drop in efficiency seen at high pT for

moderate isolation constraints demonstates why it is sensible for a menu to include

high pT non-isolated triggers. These maintain higher efficiency triggering where rate

reduction is not as critical as for lower pT.


Repeating the analysis, with the same cluster threshold and isolation cuts, for a

centre of mass energy of 7 TeV produced the results shown in Fig. 4.8. Again the

prompt taus in the tt̄ sample were used.

Comparison of Fig. 4.8 to Fig. 4.7 reveals a dramatic difference. The softening of

the turn on curve was discussed in 4.4.1, however what is immediately apparent is

that for the 7 TeV sample the effect of applying the isolation constraint has been

significantly reduced. Whilst a slight fall in efficiency is present for the tighter of

the EM and hadronic isolation conditions, particularly at large values of the truth

visible pT of the tau, the 6 GeV EM isolation cut and the 5 GeV hadronic isolation

cuts have very little effect on the trigger efficiency (when compared to the case with

no isolation applied) as a function of the visible pT. For EM isolation, the value

at which full efficiency is reached is moved to slightly larger pT than for the case

79

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(b)

Figure 4.8: Plots of tau trigger efficiency versus truth visible pT, with isolation applied,

for prompt taus in the tt̄ process for a centre of mass energy of 7 TeV. The left plot shows

the effects of 4 and 6 GeV cuts on EM isolation while the right plot shows the effect of 2

and 5 GeV cuts on hadronic isolation

with no isolation applied, but there is then no notable fall-off in efficiency. It is

expected that this is again largely due to the lowering of the calibration gains and

in particular the increase in the trigger tower noise cuts. Combined, these mean

that for a cluster of given energy, the size of the signal observed by the trigger in the

isolation region is smaller for the revised settings in the 7 TeV samples. Therefore, a

given tau is less likely to fail the same isolation theshold in the 7 TeV case than in the

14 TeV case. Consequently it would appear that for a given tau cluster threshold,

it is possible to apply tighter isolation constraints on LVL1 tau trigger for the more

recent samples with an LHC centre of mass energy of 7 TeV than was the case for

the older samples with a centre of mass energy of 14 TeV. Indeed, as the changes to

the trigger configuration will also reduce the isolation ring ET sums for background

jets, tighter isolation cuts would therefore be needed to equivalently reject the same

80

backgrounds in the newer samples.

4.4.3 Comparison of isolation effects for tt̄ and Z → τ τ

events

An area of particular interest was the comparison of the effect of the isolation cuts

on the clean Z → τ τ sample and the complicated tt̄ sample. The same isolation

cuts given in 4.4.2 were used and applied to both samples in the same way as before.

Initially, only the prompt truth taus in the tt̄ sample were used. The effect of the

five EM isolation and five hadronic isolation cuts when applied to the two samples

is shown by Fig. 4.9 for a centre of mass energy of 14 TeV.


In order to identify any differences between the samples a cut by cut comparison

was carried out. Here the efficiency of the two samples was plotted on the same axes

independently for each of the EM and hadronic isolation cuts, thereby permitting

the Z → τ τ and tt̄ efficiency curves to be compared directly for each cut. The

EM isolation cut by cut plots are shown by Fig. 4.10 and the equivalent hadronic

isolation plots are shown by Fig. 4.11.

The effect of applying isolation on the trigger efficiency can be seen to be slightly

larger for tt̄ events than for Z → τ τ events. The difference between the samples

is more noticable when considering EM isolation, with the splitting largest in the

81

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tHdIsol t

Figure 4.9: Plots of tau trigger efficiency as a function of the truth visible pT with isolation applied for Z → τ τ and tt̄ processes. A range

of EM and hadronic isolation cuts are shown. The samples used had an LHC centre of mass energy of 14 TeV

82

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Figure 4.10: Cut by cut comparison of tau trigger efficiency versus truth visible pT with EM isolation applied for the Z → τ τ and tt̄

processes (prompt truth taus used for the tt̄ sample) for a centre of mass energy of 14 TeV

83

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Figure 4.11: Cut by cut comparison of tau trigger efficiency versus truth visible pT with hadronic isolation applied for the Z → τ τ and tt̄

processes (prompt truth taus included for the tt̄ sample) for a centre of mass energy of 14 TeV

84

region between approximately 25 and 40 GeV (in the early part of the efficiency

plateau region for a fixed tau cluster threshold of 25 GeV). This appears to become

smaller as pT is increased above 40 GeV, although the size of the error on the

efficiency also starts to grow significantly. Also clearly visible, for both EM and

hadronic cases, is that as the size of the isolation cut is increased, loosening the

constraint, the separation observed between the tt̄ and Z → τ τ efficiency traces

is reduced. This is consistent with the fact that when no isolation cuts are applied

there is no obvious process dependence of the tau trigger, demonstrated by Fig. 4.5.

As described in 4.4, for the tt̄ sample possessed, ∼82% of the truth taus in the range

|η| < 2.5 which were well matched to an RoI were prompt taus. The analysis was

re-run for the tt̄ sample but calculating the trigger efficiency versus truth visible pT

for all taus within the sample. The resulting cut by cut plots are shown by Fig. 4.12

and Fig. 4.13 for the EM isolation and hadronic isolation cases respectively.

It is apparent that the act of plotting all the truth taus in the tt̄ sample reduces

the trigger efficiency observed, further separating the performance from that seen

for the Z → τ τ events. This is not entirely surprising as any taus produced from

B-mesons in tt̄ events would be expected to lie in the centre of a B-jet and as such

are therefore unisolated. The reduction observed is more significant for the case

of EM isolation as this is where the largest difference was observed previously. As

before the discrepancy remains visible between the two samples for EM isolation

cuts up to 8GeV. For hadronic isolation, the distinction is also increased between

the Z → τ τ and tt̄ samples.

85

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87


As seen in 4.4.2, the effect of a fixed isolation cut for a given cluster threshold on

the 7 TeV samples is significantly reduced compared to the 14 TeV samples. This

is reinforced by the cut by cut comparison for the 7 TeV tt̄ and Z → τ τ samples

shown in Fig. 4.14 and Fig. 4.15 (using the prompt taus in the tt̄ case). Compared

to the equivalent 14 TeV plots in Fig. 4.10 and Fig. 4.11 what is most striking is

that the significant splitting previously seen is no longer observed for all values of

the EM and hadronic isolation cuts. While the turn on for the tt̄ events remains

softer than for Z → τ τ , as can be seen for visible pT between 10 and 30 GeV, the

efficiency for prompt taus in tt̄ events in the plateau region is well modelled by the

taus in the Z → τ τ events. Consequently, LVL1 tau trigger efficiencies measured

from data for Z → τ τ events (for similar trigger conditions) should provide a good

estimate of the trigger efficiency in the plateau region for prompt taus in tt̄ events

for an LHC collision centre of mass energy of 7 TeV. This applies for both isolated

and non-isolated triggers (for the case of 14 TeV samples, tag and probe would allow

a good estimate of the non-isolated triggers only). A caveat is that it is likely the

reason for the reduced separation is a consequence of the overall reduced effect of

the isolation cuts in the 7 TeV samples (as a consequence of the higher noise cuts

and adjusted calibration). Therefore, if a tightening of the isolation cuts is required

in order to control trigger rates, it is possible that the splitting seen in the 14 TeV

samples could return (more likely for very tight isolation cuts).

88

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90

4.4.4 Examining the effect of jets for tt̄ events

A check was made on whether the effect of applying isolation has a different effect

on the tau trigger efficiency for fully leptonic tt̄ events when compared to a mixture

of semileptonic and dileptonic tt̄ events. The dileptonic events contain two fewer

light quark jets than the semileptonic ones. There were two motivations behind this

comparison. Firstly, it was intended to check whether overlap of the tau with light

quark jets was the reason for the reduced efficiency in tt̄ events, compared to Z → τ

τ events, when isolation was applied. If this were the case the trigger efficiency would

be expected to be higher for the dileptonic only tt̄ events when running isolation.

Secondly, looking at the difference between the two tt̄ event types would test the

idea that dileptonic tt̄ events could be used to study the tau trigger efficiency in

semileptonic events if the differences between the two were to be small. Equivalent

efficiency plots were produced using taus coming from dileptonic tt̄ events only,

both for the case where all the taus were considered and for the case where only

the prompt taus were used. Again the equivalent cut by cut comparison plots were

produced to examine any differences in the trigger efficiency curves that may have

been produced as a result of using the two differing tt̄ channels. Fig. 4.16 and Fig.

4.17 show the results produced when the dileptonic tt̄ event tau trigger efficiencies

were compared to those for mixed semileptonic and dileptonic tt̄ events, using the

prompt taus only.

No difference was observed, within errors, between the efficiencies produced when

only semileptonic tt̄ events were used and those produced when only dileptonic tt̄

91

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Figure 4.16: Cut by cut comparison of τ trigger efficiency versus truth visible pT with EM isolation applied for dileptonic tt̄ events and

mixed semileptonic and dileptonic tt̄ events (truth prompt taus only used for the tt̄ sample). Plots produced for a centre of mass energy of

14 TeV.

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Figure 4.17: Cut by cut comparison of τ trigger efficiency versus truth visible pT with EM isolation applied for dileptonic tt̄ events and

mixed semileptonic and dileptonic tt̄ events (truth prompt taus only used for the tt̄ sample). Plots produced for a centre of mass energy of

14 TeV.

93

events were used. This was the case for all values of the EM and hadronic isolation

cuts. Using all the taus produced irrespective of their origin also yielded the same

result. Equivalent results were also observed when using the 7 TeV tt̄ sample.

4.4.5 Early Tau Trigger Menu

A preliminary study was carried out using the Level 1 section of a proposed 1031 cm−2 s−1

early data-taking trigger menu of ATLAS as it was expected to be during 2008. Only

the 21 pure tau trigger items within the menu were examined. Table 4.1 shows the

proposed LVL1 tau trigger items together with their corresponding cuts on the tau

cluster energy and EM isolation energy where appropriate. No hadronic isolation

requirement featured in the menu. Similarly, table 4.2 shows the 21 items for the

whole trigger menu that contained pure tau components only at LVL1, together

with their LVL1 content and prescale. All the thresholds and prescales used in this

menu were based on 14 TeV Monte Carlo.

Using the same tt̄ samples as before, the fraction of events passing each of the LVL1

tau trigger thresholds was obtained. This is illustrated in Figure 4.18 for both 14 TeV

and 7 TeV, which does not take prescaling into account. As would be reasonably

expected, the fractions passing the low energy thresholds are similar for the two

different centre of mass energies. The acceptance of L1 TAU25 and L1 TAU40 is

notably lower for the 7 TeV sample. As the turn on curves for the different trigger

thresholds overlap, this is again likely to be as a result of the softening and shift

in the turn on produced by the revised calibration used in the 7 TeV samples. In

94

Item name TauClus[GeV] EmIsol[GeV]

L1 TAU5 >5 Off

L1 TAU6 >6 Off

L1 TAU9I >9 ≤6

L1 TAU11I >11 ≤6

L1 TAU16I >16 ≤6

L1 TAU25 >25 Off

L1 TAU25I >25 ≤6

L1 TAU40 >40 Off

Table 4.1: LVL1 trigger items

the trigger menu used during 2010 running this was accounted for by retaining

the lower thresholds studied here (L1 TAU5, L1 TAU6 and L1 TAU11I), whilst

replacing L1 TAU25 and L1 TAU40 by L1 TAU20 and L1 TAU30 respectively.

Tau Threshold

L1_T

AU5

L1_T

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I

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Figure 4.18: Fraction of events passing the eight LVL1 tau thresholds when running over

a mixture of dileptonic and semileptonic tt̄ events. No prescaling has been applied

95

Item name L1 Item content L1 Prescale

tauNoCut L1 TAU5 1×107

tau10 L1 TAU6 1500

tau10i L1 TAU6 1500

tau15 L1 TAU6 1500

tau15i L1 TAU6 1500

tau15i PT L1 TAU6 1500

tau20i L1 TAU9I 1×106

tau25i L1 TAU11I 1500

tau35i L1 TAU16I 1×106

tau45 L1 TAU25 8

tau45i L1 TAU25I 4

tau60 L1 TAU40 1

tau100 L1 TAU40 1

twotau15i L1 2TAU6 100

twotau25i L1 2TAU9I 1

twotau25i PT L1 2TAU9I 1

twotau35i L1 2TAU16I 1

tau15i tau35i L1 2TAU6 TAU16I 1

tau15i tau35i PT L1 2TAU6 TAU16I 1

tau10i tau45 L1 2TAU6 TAU25 1

tau15i tau45 L1 2TAU6 TAU25 1

Table 4.2: Pure tau trigger items

96

By looking at the number of RoIs passing each Level 1 threshold for each event,

the overall fractional acceptance was deduced for the threshold combination corre-

sponding to the Level 1 part of each tau trigger item. Acceptances were calculated

both before and after the application of the appropriate Level 1 prescales, and these

two cases are illustrated in Fig. 4.19 and Fig. 4.20 for the 14 and 7 TeV cases respec-

tively. It should be noted that the prescales studied here can only be considered an

example of a typical set (with large prescales for the low ET items and prescale fac-

tor reducing with increasing ET) as trigger menus are under constant development

at ATLAS, with both thresholds and prescales evolving over time.

For both sets of plots it can be seen that when prescales are applied the minimum

threshold which still accepts events at Level 1 is tau45. Any triggers which have

a single LVL1 tau threshold below 25 GeV are almost completely removed by the

LVL1 prescales. This emphasises the need to use combined LVL1 triggers, such as

tau + missing ET, when low tau thresholds are required for high luminosities. As

would be expected, the items containing the higher LVL1 thresholds are less efficient

for the 7 TeV events than for 14 TeV events due to the effect of the tau pT spectrum.

The acceptances shown in Figures 4.18, 4.19 and 4.20 were calculated using RoI

produced for all events in the tt̄ sample known to contain a truth tau of any origin.

Acceptances were also calculated for all events in the tt̄ sample regardless of whether

a truth tau was actually present. No significant alteration to the acceptance was

observed for those thresholds which are unprescaled at Level 1.

97

Tau Items

tauNoCuttau10tau10itau15tau15i

tau15i_PTtau20itau25itau35itau45tau45itau60

tau100twotau15itwotau25i

twotau25i_PTtwotau35i

tau15i_tau35itau15i_tau35i_PT

tau10i_tau45tau15i_tau45

Fraction of Events

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4.5 Conclusions

A study into the performance of the ATLAS LVL1 tau trigger has been described

using Monte Carlo truth information. Two samples were used to allow the perfor-

mance in the complicated environment of tt̄ events to be compared to that seen in

clean Z → τ τ events. Performance was compared before and after the applica-

tion of a series of fixed EM and hadronic isolation cuts. Using 14 TeV centre of

mass energy samples produced in Athena release 12.0.6 a process dependence of the

tau trigger was observed when isolation was applied. Repeating the analysis for

equivalent 7 TeV centre of mass energy samples, containing a more realistic trigger

simulation, in Athena release 15.6.13.7 showed this process dependence to have been

almost completely removed for the same threshold and isolation settings. It was de-

duced that in such a scenario a measurement of the tau trigger efficiency from data

(via tag and probe techniques) for Z → τ τ events could provide a good estimate of

the LVL1 tau trigger efficiency for prompt taus in tt̄ events. Similarly, a measure of

the efficiency in dileptonic tt̄ events, where a tag and probe technique could be used,

was seen to provide a way of estimating the LVL1 efficiency for taus in all tt̄ events.

Finally, an example of a typical ATLAS tau trigger menu was examined for both

centre of mass energies, revealing the need to use combined triggers to select low

energy taus at LVL1 at the luminosities the LHC is expected to reach in 2011-2012.

99

Chapter 5

Hadronic Tau Identification for

Early ATLAS Data

5.1 Introduction

Contained within this chapter are the details of an investigation into the various

possibilities for identification of hadronic tau decays in early ATLAS data. The

ATLAS tau physics working group designated a series of approved ‘Safe Cuts’ in-

tended to identify such taus based on a number of either calorimeter only or com-

bined calorimeter and tracking variables [47]. These cuts had been optimised on

a comparatively clean signal sample. The work covered here therefore evaluates

the suitability of the cuts for use in complicated top events, and compares their

performance to two different single variable cuts.

100

5.2 Good Tau Selection

Before considering the details of making a tau selection, it is necessary to note which

of the tau decays can be realistically expected to be observed as distinct objects with

the ATLAS detector. When a tau decays to leptons, the only difference to direct

lepton production is the presence of the two neutrinos as detailed in 1.7.2. As the

neutrinos leave no signature in the ATLAS detector other than contributing to a

level of missing energy, which is expected to be present already in many interesting

LHC physics signatures, it is generally considered unrealistic to identify the leptonic

tau decay modes. The tau to lepton decay is therefore accounted for as part of

the electron and muon branching fractions for a given decay. For example, the

decay t → W → τ → l is included in the case t → W → l in tt̄ cross-section

measurements [48].

Tau identification in ATLAS concentrates on identifying the hadronic decay modes.

The key is to distinguish jets originating from a hadronically decaying tau from

those originating from quarks or QCD. In a practical sense, this relies on identifying

taus as narrow jets with a low track multipicity. Jet width is usually determined in

two ways. The first involves measuring the spread of the shower the jet produces

in the detector calorimeter, either in a particular layer, or by combining different

measurements across the various calorimeter layers. Alternatively, jet isolation can

be used. Here typically a cone is defined of a chosen width to represent the core

region of the jet (where the majority of the energy would be expected to lie). A

second isolation cone (or other chosen region) is then defined around the jet core,

101

as shown in Fig. 5.1. By measuring the ratio of the energy found in the two cones a

judgement can be made on the jet width, with wider jets having larger fractions of

their total energy found in the isolation cone. Jet track multiplicity comes simply

from looking at the number of charged tracks assigned to the jet.

Figure 5.1: Hadronic tau decays produce a jet with an energy cluster which is typically

narrower than an equivalent QCD jet. Tau candidates can in principle be distinguished

by measuring the width of the shower, the energy in some defined isolation region around

the jet, and by the track multiplicity within the jet

The key of such a hadronic tau selection is to ensure a strong rejection against QCD

jets, while retaining the maximum number of tau candidates. In order to ensure

the best possible separation between taus and background jets, higher multiplicity

tau decays of five prongs and above are disregarded. Furthermore, the 1-Prong and

102

3-Prong modes are also often considered separately, and a wide range of different

calorimeter and track variables are usually combined together in each case (often

using multivariant techniques) in order to produce the best discrimination between

signal taus and background jets.

5.3 Tau Reconstruction in ATLAS

The ATLAS experiment uses two different methods for reconstruction of possible

hadronic tau candidates. One algorithm starts from tracking information combined

with quality cuts, while the second builds candidates from calorimeter clusters via a

cone algorithm [49]. Historically the two tau reconstruction algorithms were distinct

from each other, with the possiblity that the same tau could be reconstructed via

both algorithms independently. The primarily calorimeter based algorithm was

known as TauRec and the lead track based algorithm Tau1P3P [50]. More recently

the two tau reconstructions have been combined from release 14.0.0 of the ATLAS

reconstruction software [51]. One set of reconstructed tau candidates are therefore

now produced, but with each tau candidate flagged as being either ‘calo-seeded’ (ex.

TauRec), ‘track-seeded’ (ex. Tau1P3P) or ‘calo-and-track-seeded’. The ‘calo-seeded’

candidates are devised from calorimeter topological clusters (these sum neighbouring

calorimeter cells, based on the significance of the energy found within each cell [52])

with ET > 10 GeV [47] while the ‘track-seeded’ candidates originate from a track

possessing pT > 10 GeV [49].

103

5.4 Hadronic Tau Identification by Safe Cuts

5.4.1 Safe Cuts

An assortment of different techniques has been developed for tau identification with

the ATLAS detector. Many of these use large numbers of variables combined and

tuned via multivariant techniques as summarised in [49]. In early ATLAS comis-

sioning and running it is expected that the inputs into these tools will not be fully

optimised, particularly with regards to tracking variables. As such a set of desig-

nated ‘Safe Cuts’ have been developed by the ATLAS tau physics working group for

hadronic tau identification. These are based on a small number of so called ‘robust

variables’ [47] which are expected to be comparatively well understood in early LHC

running.

The safe cuts were optimised using ATLAS datasets produced by the Pythia event

generator with a centre-of-mass energy of 14 TeV [47]. A relatively clean signal

sample of taus was used in the form of two datasets combined together, the first being

Z → ττ and the second bbA → bbττ (with mA =800 GeV) [47], while a background

was provided via dijet samples in an approximate equivalent pT region [47].

Two sets of safe cuts were provided by the tau working group. The first used four

calorimeter variables only and was considered the more robust approach. The second

set used a combination of calorimeter and track variables. In the case of the former,

the cuts were applicable to any calorimeter seeded tau candidates, while for the

latter the cuts could be applied to the calorimeter and track seeded taus only [47].

104

5.4.2 Safe Variables

The calorimeter only safe cuts used a combination of the variables given below [53] [54];

• Combined radius in whole EM calorimeter (EmRadius)

• Isolation fraction in whole calorimeter (IsolationFraction)

• Width in the strip layer of calorimeter (stripWidth2)

• Ratio of EM to total calorimeter energy (ET(EM)/ET)

The combined calorimeter and track selection safe cuts relied on a total of nine

variables [53] [54];

• The existing four calorimeter only variables listed above

• Angular spread of tracks, weighted by transverse momentum in multi-track

candidates (RWidth2Trk3P)

• Ratio of the (ET) to the (pT) of the lead track in the candidate (etOverPtLead-

Track)

• Ratio of the summed hadronic ET to the summed pT of the (up to three)

highest pT tracks (etHadCalib/ptTrack1 + 2 + 3)

• Ratio of the summed EM ET to the summed pT of the (up to three) highest

pT tracks (etEMCalib/ptTrack1 + 2 + 3)

105

• Ratio of the summed pT of the (up to three) highest pT tracks to the total com-

bined calibrated summed EM and hadronic ET (ptTrack1+2+3/(etEMCalib1+

2 + 3etHadCalib))

5.4.3 Calorimeter Only Variable Definitions

Depending on the seed of the tau candidate, the variables possessed by the object

were defined differently. As the safe cuts were designed for the calo-seeded taus, the

calorimeter only safe cut variables were therefore defined in accordance with this.

The first three variables were taken directly from the reconstructed AOD container

and are given as:

• EmRadius : Uncalibrated ET weighted radius in the Presampler + EM1 + EM2

within dR < 0.4

• IsolationFraction : Ratio of the uncalibrated ET of cells within 0.1 < dR < 0.2

and cells within 0 < dR < 0.4

• stripWidth2 : Uncalibrated ET weighted width in the strip layer within dR < 0.4

The fourth variable was the ratio of the EM to the total calorimeter energy which

was calculated by;

Energy Ratio =etEMCalib

etEMCalib + etHadCalib(5.1)

106

where etEMCalib and etHadCalib are the calibrated EM ET and hadronic ET re-

spectively. Fig. 5.2 illustrates the distributions produced for these four variables in

tt̄ events, plotted for both reconstruced tau candidates matched to (1-Prong and

3-Prong) Monte Carlo truth taus (black) and fake candidates which are therefore

not matched to truth (in red). The matching definition used to make the plots

is described in 5.4.4. As can be seen, the separation between the good and fake

distributions is limited, with EmRadius and IsolationFraction appearing the better

discriminators.

5.4.4 Safe Cut Optimisation

Development of the two sets of safe cuts has been fully described elsewhere [53] [54]

and so will not be described here. For both the calo. only and the calorimeter

plus track scenarios the same basic technique was used. Using a generic algorithm

to separate the signal and the background distributions [53], cuts were produced

separately for one and three prong taus and in 5 discrete pT bins of 10-25 GeV, 25-

45 GeV, 45-70 GeV, 70-100 GeV and >100 GeV [47]. Loose, medium and tight tau

selections were defined as producing signal selection efficiencies of 30%, 50% and 70%

respectively, where the signal selection efficiency was defined as in equation 5.2 [47],

with NPassMatched being the number of matched reconstructed n-prong tau candidates

passing the cuts and NTotalMC the number of n-prong Monte Carlo tau leptons within

the pT range with stable daughters.

107

emRadius0 0.05 0.1 0.15 0.2 0.25 0.3

-1Ev

ent

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035Truth matchedUnmatched

(a) EmRadius

isolationFraction0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1Ev

ent

0

0.01

0.02

0.03

0.04

0.05

0.06

Truth matchedUnmatched

(b) IsolationFraction

stripWidth20 0.01 0.02 0.03 0.04 0.05 0.06 0.07

-1Ev

ent

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07 Truth matchedUnmatched

(c) StripWidth2

EnergyRatio0 0.2 0.4 0.6 0.8 1

-1Ev

ent

0

0.01

0.02

0.03

0.04

0.05

0.06 Truth matchedUnmatched

(d) Energy Ratio

Figure 5.2: Distribution of good and fake hadronic taus, normalised to unit area, for the

four variables of the calorimeter only ‘safe cuts’. In these plots good taus are matched to

truth with dR < 0.2, fakes have dR > 0.5 from the nearest truth tau

108

εn−prongτ =

NPassMatched

NTotalMC

(5.2)

Here ‘matched’ means that the separation between the reconstructed tau candidate

and the true hadronic tau has a ∆R value smaller than 0.2, while the hadronic Monte

Carlo tau definition excluded those decaying to final state kaons (although the effect

of these being allowed was checked and seen to be tiny). The set of calo. only safe

cuts evaluated within this chapter are given in Appendix A, with tables A.1 and A.2

showing the cut values applied for one prong and three prong selections respectively.

5.5 Evaluation of Calo. Only Safe Cut Efficiencies

in tt̄ Events

The remainder of this chapter will concentrate on an evaluation of the performance

of the calorimeter only safe cuts with respect to the selection of hadronic 1 and 3

prong taus in tt̄ semileptonic and dileptonic events for an LHC centre-of-mass energy

of 10 TeV. The study was carried out using release 14.5.0 of the ATLAS Athena

software and Monte Carlo simulated data samples produced in release 14.2.25.6 as

part of the mc08 collection of 10 TeV samples. Calorimeter only cuts were considered

for two reasons. Firstly, cuts were being examined with the intention to use them

in the top physics area for the first year of ATLAS data taking. Consequently,

the extra simplicity of the calorimeter only cuts was preferable. Secondly, with the

merging of the two tau reconstruction types as discussed in section 5.3, some of the

109

tracking variables used in the calorimeter and track safe cuts were to be replaced

from release 15 of the ATLAS software [54]. Although this analysis was carried out

in an earlier software release, as the first ATLAS collision data was to be produced in

release 15 it was sensible to only consider a selection that could be carried forwards

unchanged.

5.5.1 Efficiency with respect to Monte Carlo

The first stage of the study focused on a direct comparison of the signal selection

efficiency for the safe cuts in tt̄ 1 events relative to that produced for a combination

of Z → ττ 2 and bbA → bbττ (mA =800 GeV) 3 events. The purpose of this was

to evaluate how the hadronic tau selection efficiency was affected by the move to a

more jet dominated environment and to establish whether it would be realistic to

use the safe cuts for tau identification in tt̄ events. The combination of the latter

two datasets was intended to match as far as possible for 10 TeV samples the signal

datasets used at 14 TeV to optimise the safe cuts [47]. At all stages each set of cuts

was applied manually by hand for each of the safe cut pT bins, while for all three

samples sufficient dataset sizes were used to give negligible errors on the selection

efficiencies. For the tt̄ and Z → ττ samples 400,000 events of each were used, while

for the bbA → bbττ case the entire available dataset was processed comprising a

total of 90,400 events.

1Sample mc08.105200.T1 McAtNlo Jimmy.merge.AOD.e357 s462 r635 t532Sample mc08.106052.PythiaZtautau.merge.AOD.e347 s462 r635 t533Sample mc08.106573.PythiabbAtautauMA800TB35.merge.AOD.e347 s462 r635 t53

110

As an initial comparison, the tau selection efficiency in the samples was calculated as

per that given in equation 5.2 as used to optimise the safe cuts. Tau candidates were

considered to be well matched to truth hadronic taus if they produced a ∆R value

less than 0.2. For combining the Z → ττ and bbA → bbττ results the efficiency was

formed by requiring both the denominator and numerator of the calculation to be

the sum of the number of events from the two samples. Fig. 5.3 shows the resulting

tau selection efficiency for the tt̄ sample and mixed Z → ττ and bbA → bbττ sample.

The efficiency was calculated separately for each of the five pT bins (with the bins

defined in term of the truth visible pT) and is shown independently for 1-Prong and

3-Prong taus as well as being divided into loose, medium and tight selections.

By examining the plots it can be seen that for the efficiency definition used the

values produced for the tt̄ sample are slightly smaller (typically 5-10%) than for

the combined Z → ττ and bbA → bbττ sample. An exception is the >100 GeV

bin for the medium and tight cases, where the control sample efficiency is noteably

larger, however this is the region where the bbA → bbττ events start to dominate the

combined sample. There will be very few taus produced in this bin by tt̄ events in

early 7 TeV ATLAS data, and those that are can only be produced by highly boosted

top quarks. This aside, the patterns match well for the two samples thoughout for

both 1-Prong and 3-Prong taus and for each of the cut levels. The cut hierarchy

also remains correct for the tt̄ sample with the loose cut efficiency higher than the

medium, which is in turn larger than for the loose selection. This is true for all the

pT bins in both 1-Prong and 3-Prong cases.

111

Figure 5.3: Selection efficiency comparison between tt̄ and combined Z → τ τ and A → τ τ events for the calorimeter only tau safe cuts.

Comparisons are split into loose medium and tight cuts (shown by columns running from left to right), and 1-Prong and 3-Prong hadronic

taus

112

5.5.2 Efficiency with respect to Reconstructed Taus

While defining the efficiency as per 5.5.1 is interesting because it shows how the

overall tau selection performs, it is not necessarily the best way of examining the

performance of the tau selection cuts themselves. This is because the cut efficiency

and the reconstruction efficiency are folded in together (the reconstruction efficiency

being the probability for a real tau to pass the loose criteria used to define a tau

candidate and so be found in the tau container for the event). To examine the cut

efficiency alone (which also allows for easier comparison with other techniques as

discussed in section 5.7) it is possible to define the signal selection efficiency in a dif-

ferent way, via equation 5.3. Here NPassMatched is the number of matched reconstructed

n-prong tau candidates passing the cuts (as before), while NTotalMatched is the number of

matched reconstructed n-prong tau candidates present before the cuts.

εn−prongτ =

NPassMatched

NTotalMatched

(5.3)

The same procedure as in section 5.5.1 was followed to compare the tt̄ signal selection

efficiency to that for the combined Z → ττ and bbA → bbττ sample separately for

1-Prong and 3-Prong taus for the same five pT bins, but where the efficiency was

now as defined in 5.3. In addition, while the matched Monte Carlo truth taus were

still used to define the prong of the candidate, the pT binning was now based on

the reconstructed pT of the tau candidates. Table 5.1 shows the resulting values for

1-Prong taus whilst table 5.2 shows the equivalent results for 3-Prong taus.

113

Examining the two tables and comparing to Fig. 5.3, it can be seen that in certain

pT bins the safe cuts are actually carrying out little of the discrimination between

the actual and fake taus; for example the 1-Prong >100 GeV bin where the loose

efficiency is 0.99 and 0.98 for the two samples respectively (although the combined

cut and reconstruction efficiency is also very high). In other areas the cut efficiencies

relative to the reconstruction are much lower and so the safe cuts are providing a

larger proportion of the discrimination, as demonstrated by the 1-Prong 10-25 GeV

medium values.

Comparing the efficiencies, with respect to the reconstructed taus, for tt̄ events

versus those for the combined samples a similar pattern is present to that observed

in 5.5.1. For the 45-70 and 70-100 GeV bins the tt̄ selection efficiency is seen to

be approximately 10% lower than for the combined control sample for all cut levels

and for both for 1-Prong and 3-Prong taus. In the other pT regions the performance

is not quite as stable. As would be expected the efficiencies for tt̄ most closely

compare with those for the cleaner sample in the loose cuts, with the tt̄ performance

dropping as the cut level is tightened. Looking at the 10-25, 25-45 and >100 GeV

bins for the 3-Prong case in table 5.2, it can be seen that the efficiency for the

tight selection is approximately 10-15% lower than for the medium selection, which

is then lower than for the loose selection by approximately the same amount. The

loose selection for the two low pT bins is again seen to be approximately 5-10% lower

for tt̄ than for the clean sample, which increases to around 15% for the >100 GeV

bin. By contrast the 1-Prong case does not behave in such a predictable manner.

Examining the 25-45 GeV bin the loose cut efficiency for the tt̄ sample is only

114

approximately 15% lower than for the control sample. Performance for the medium

and tight efficiencies is then approximately a further 10% worse for the tt̄ compared

to the combined Z → ττ and bbA → bbττ sample. The same pattern is repeated for

the 10-25 GeV bin but with the starting point for the loose selection having the tt̄

efficiency 30% lower than for Z → ττ and bbA → bbττ . In the >100 GeV bin the

performance is practically identical for the two samples when looking at the loose

selection, with the tt̄ falling away to 60% and 50% of the Z → ττ and bbA → bbττ

effciency for the medium and tight cases.

For the purpose of top physics, the bins which are the most important are those

covering the pT range from 25-100 GeV. Taking the figures in the two tables as a

whole, it can be seen that the performance of the safe cut efficiency with respect

to the reconstruction for the tt̄ sample holds up well compared to the Z → ττ and

bbA → bbττ sample in this region.

115

pT[GeV] CutLevelTau efficiency for Z and A Tau efficiency for tt̄

Efficiency Ratio

TauRec Before/After TauRec Before/After

10-25

Loose 0.69 0.48 0.70

Medium 0.36 0.19 0.53

Tight 0.20 0.10 0.50

25-45

Loose 0.73 0.60 0.82

Medium 0.41 0.30 0.73

Tight 0.23 0.16 0.69

45-70

Loose 0.78 0.73 0.93

Medium 0.43 0.39 0.91

Tight 0.19 0.18 0.93

70-100

Loose 0.96 0.95 0.98

Medium 0.48 0.43 0.90

Tight 0.25 0.24 0.94

>100

Loose 0.99 0.98 0.99

Medium 0.63 0.36 0.58

Tight 0.32 0.16 0.49

Table 5.1: Hadronic 1-Prong tau selection efficiency with respect to reconstructed taus.

Efficiencies are shown for a combined sample of Z → τ τ and A → τ τ events and for tt̄

events

116

pT[GeV] CutLevelTau efficiency for Z and A Tau efficiency for tt̄

Efficiency Ratio

TauRec Before/After TauRec Before/After

10-25

Loose 0.95 0.92 0.97

Medium 0.74 0.64 0.86

Tight 0.32 0.20 0.64

25-45

Loose 0.89 0.84 0.93

Medium 0.48 0.37 0.77

Tight 0.26 0.17 0.64

45-70

Loose 0.75 0.72 0.96

Medium 0.43 0.39 0.90

Tight 0.18 0.16 0.89

70-100

Loose 0.99 0.97 0.99

Medium 0.49 0.42 0.86

Tight 0.27 0.22 0.82

>100

Loose 0.91 0.75 0.83

Medium 0.85 0.61 0.72

Tight 0.36 0.14 0.39

Table 5.2: Hadronic 3-Prong tau selection efficiency with respect to reconstructed taus.

Efficiencies are shown for a combined sample of Z → τ τ and A → τ τ events and for tt̄

events

117

Background Rejection Factor

When considering the cut performance relative to the reconstruction, it is also pos-

sible to obtain a measure of the rejection of the fake taus contained within a given

sample. A rejection efficiency can be defined as per equation 5.4, from which a

rejection factor can then be calculated by equation 5.5. In the former, NPassUnmatched is

the number of reconstructed candidates not matched to an n-prong Monte Carlo tau

remaining after the cuts, whereas NTotalUnmatched is the number of reconstructed n-prong

candiates not matched to an n-prong Monte Carlo tau present before the cuts were

applied.

εn−prongFake τ =

NPassUnmatched

NTotalUnmatched

(5.4)

RejectionFactor =1

εn−prongFake τ

(5.5)

It is possible to calculate the rejection for any number of different samples providing

a source of fake taus. For the purpose of this study, where the aim was identifying

taus in tt̄ events, the internal fakes within the tt̄ sample were used as background.

Again using the calorimeter only safe cuts, rejection factors were calculated for the

tt̄ sample. The same five pT bins were used as in 5.5.2 with numbers produced

separately for 1-Prong and 3-Prong taus for the loose, medium and tight selections.

The resulting rejection factors are shown in table 5.3 for both the 1-Prong and

3-Prong taus.

Examining the table, it can be seen that in general the rejection achieved is higher in

118

the 1-Prong case than in the 3-Prong case. Moving through the cut levels from loose

to medium to tight, the rejection increases as would be expected for both prongs. In

addition, as the cuts are tightened, the rejection for the 1-Prong tt̄ events increases

slightly relative to that for the 3-Prong.

pT[GeV] Cut LevelRejection for tt̄

1-Prong Before/After 3-Prong Before/After

10-25

Loose 2.86 1.15

Medium 7.92 1.64

Tight 14.57 3.77

25-45

Loose 5.21 1.65

Medium 15.88 4.97

Tight 26.41 9.69

45-70

Loose 6.68 2.78

Medium 24.27 9.82

Tight 42.01 21.05

70-100

Loose 1.68 1.23

Medium 32.90 14.56

Tight 44.68 26.16

>100

Loose 1.11 8.76

Medium 51.48 13.74

Tight 77.55 62.08

Table 5.3: Hadronic 1-Prong and 3-Prong jet rejection factors for inter sample background

events in tt̄ events

119

Significance in Top Events

A further examination of the performance of the safe cuts in the tt̄ sample can be

made by defining a significance. This was calculated via equation 5.6 where NPassMatched

and NPassUnmatched were as defined previously.

Significance =NPass

Matched√

(NPassMatched) + (NPass

Unmatched)(5.6)

The significance was calculated for the arbitrary sample size of 400,000 events and

considered only the ‘in sample’ background provided by the possible fake taus within

the tt̄ events. Nevertheless, examining the values shown in table 5.4 it can be seen

that, whilst tightening the safe cut level increases the background jet rejection as

described in 5.5.2, the corresponding drop in the tau selection efficiency is suffi-

cienctly large that proportion of signal to background in the sample drops. The

only exception is the medium cut for 1 and 3-Prong taus in the 70-100 GeV bin,

which has a higher significance than the loose cut. Significance remains lower for the

tight cut than for the medium cut in this bin however. As an overall consequence,

depending on the size of the data sample available, it may be preferable to run a

looser selection than may be optimal for background rejection in order to retain a

greater proportion of the real taus in tt̄ events.

120

pT[GeV] Cut LevelSignificance

1-Prong 3-Prong

10-25

Loose 36.60 24.59

Medium 24.43 20.34

Tight 17.21 10.00

25-45

Loose 69.01 33.64

Medium 54.91 25.17

Tight 38.72 15.99

45-70

Loose 78.33 31.69

Medium 65.94 28.56

Tight 42.67 17.45

70-100

Loose 45.45 22.44

Medium 53.32 25.02

Tight 38.32 17.71

>100

Loose 31.86 26.62

Medium 41.05 25.21

Tight 25.27 12.19

Table 5.4: Significance values in tt̄ events of the 1-Prong and 3-Prong hadronic safe cut

selections

121

5.6 Calorimeter Only Safe Cut Correlations (Top

Events)

As was described in 5.4.1 the calorimeter only safe cuts used four variables, of which

EmRadius, IsolationFraction and stripWidth2 each provide a measurement of the

width of the calorimeter cluster. The correlations between the four variables of the

calorimeter only safe cuts were examined for both real and fake taus in the tt̄ sample.

As previously, good taus were identified by requiring that they were matched to a

truth 1-Prong or 3-Prong hadronic tau with a ∆R value smaller than 0.2, with the

prong being allocated based on the truth tau. Correlations were examined for all six

combinations of the four variables and separately for the 1-Prong good taus, 3-Prong

good taus and the inter-sample background fakes. The resulting distributions are

shown by figures 5.4, 5.5 and 5.6 respectively. From examining the plots it is appar-

ent that there is a significant correlation between EmRadius and IsolationFraction

for both good and fake taus. Clear correlations are also visible between EmRadius

and StripWidth2, and likewise IsolationFraction and StripWidth2. Although it is

not possible to observe a clear correlation in the plots which contain the Energy-

Ratio, it is apparent that the distribution is principally enhanced for values of the

energy ratio close to 1 and small values of the other variable.

Considering the 1-Prong and 3-Prong ‘signal’ tau plots, the distributions are seen

to take a similar shape, but with events concentrated at smaller values of EmRadius

and IsolationFraction in the case of the 1-Prong taus. When these are compared

122

to the plots for the fake taus, for the EmRadius versus IsolationFraction plot the

fake taus are seen to be concentrated at much larger values than for the 1-Prong

good taus, with the 3-Prong good taus in between. Such a clear trend is not seen in

the other distributions, therefore loosely suggesting that EmRadius and, to a lesser

extent, IsolationFraction are the two strongest discriminants of the four variables.

123

isolationFraction0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

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th2

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Figure 5.4: Correlations between the calorimeter only safe cut variables for reconstructed taus matched to 1-Prong hadronic MC taus (with

4R < 0.2) for the tt̄ sample

124


emRa

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Figure 5.5: Correlations between the calorimeter only safe cut variables for reconstructed taus matched to 3-Prong hadronic MC taus (with

4R < 0.2) for the tt̄ sample

125


emRa

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Figure 5.6: Correlations between the calorimeter only safe cut variables for reconstructed taus not matched to 1 or 3-Prong hadronic MC

taus (with 4R < 0.2) for the tt̄ sample. This therefore represents the correlations for the background fake taus within the sample

126

5.7 Performance Evaluation of a Single Cut Se-

lection

5.7.1 Motivation

Having evaluated the performance of the calorimeter only safe cuts for tt̄ events, and

compared the safe cut performance for top events to cleaner environments, the study

was extended by considering whether it would be possible to produce an equivalent

simpler tau selection via the use of only one variable. As seen, the safe cuts use

four variables, of which three are relatively well correlated as per section 5.6, which

are combined in varying ways for the different pT bins. For any given set of the

safe cuts three of the variables are doing little with regards enhancing the fake tau

discrimination.

It was hypothesized that one of these variables alone could be used to replace the

safe cut combination. To test this, the study was evolved to look at how the safe

cut performance compared to a cut on a single variable optimised for selection of

1-Prong or 3-Prong hadronic taus in the top sample. As per section 5.5.2, the fake

taus produced by the extra jets within the top sample were used to provide the

background fakes for both sets of cuts (i.e. allowing a direct comparison to be made

between the safe cuts and the proposed single cut).

Two different single variable cuts were evaluated. The first used the variable Isola-

tionFraction as the discriminant as it was considered to be the simplest of the four

127

variables, essentially being a variation on the isolation regions already used at the

trigger level. Secondly, a single variable selection was produced based on EmRa-

dius as this was considered to be the single variable that offered the best potential

separation between the good and fake tau candidates.

5.7.2 Production of cut values

In order to produce the single cut values 1-Prong and 3-Prong hadronic taus were

considered separately as for the safe cuts. For each variable two separate selections

were produced, a first which was optimised in the same five pT bins used by the

safe cuts, and a second which had a single cut for the whole pT range. Again the

pT region used was that of the reconstructed candidate. The selected variable was

plotted in the required pT region, with the distributions produced separately for

those reconstructed taus matched (with 4R < 0.2) to Monte Carlo truth hadronic

taus with the chosen prong (signal) and for those not matched to any Monte Carlo

tau.

Starting at the plot origin, the cut location was moved across the distribution bin-

by-bin from low to high values of the cut, with the signal selection efficiency and

background rejection efficiency (and hence rejection factor) calculated for each bin.

Selected taus were taken to be those with a value less than the cut value. The signal

selection efficiency was defined as per equation 5.3 as previously. The rejection effi-

ciency was defined as in equation 5.7, where the variables NTotalUnmatched and NPass

Unmatched

are as defined previously, with the rejection factor subsequently calculated as per

128

equation 5.8.

εRejectionFake τ =

NTotalUnmatched − NPass

Unmatched

NTotalUnmatched

(5.7)

RejectionFactor =1

εn−prongFake τ

=1

1 − εRejectionFake τ

(5.8)

As per the background rejection factors shown earlier in this chapter, only the

inter-signal background was considered. For tt̄ events this is effectively an n-jet

background, comprising at least two b-jets for the dileptonic channel.


-1Ev

ent

0

0.01

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0.04

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Truth matched

Unmatched


Effic

ienc

y

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Unmatched

Figure 5.7: Illustration of setting the single variable cuts. Selection efficiencies are chosen

and then background rejection factors calculated for the same bin. The right hand plot

shows how the bin is selected based on given signal selection values while the left hand

plot shows where the resulting cut appear on the signal and background distribtions

129

Efficiency definition

The three tau safe cut levels, loose medium and tight, had been chosen by their

authors to give nominal selection efficiencies of 70%, 50% and 30% respectively, as

stated in 5.4.4. These were defined relative to the Monte Carlo and not relative to

the reconstruction (as was to be the case here), while the measured efficiencies were

also seen to fluctuate slightly from the expected values for the tt̄ sample. Therefore,

to allow fair comparison between the safe cuts and a single cut selection, two different

sets of cut values were produced.

Real cut values

Signal selection efficiencies of 70% (loose), 50% (medium) and 30% (tight) were

chosen. The background rejection factors for the allocated bins were then calculated.

Figure 5.7 shows an illustration of how this was carried out. The left hand plot

shows the IsolationFraction distributions for the well matched (signal) and poorly

matched (fake) tau candidates respectively. In the right hand plot can be seen

the signal selection and background rejection efficiencies produced when the cut

location is moved bin-by-bin from 0 to 1. Marked on the plots are the locations of

cuts producing signal efficiencies of 70%, 50% and 30%. The background rejection

is then calculated from the background efficiency seen in the same bin, which can

simply be read off.

Equivalent cut values

To allow direct comparison to the safe cuts, the location of the loose, medium

130

and tight cuts was arranged so that the signal selection efficiency was matched to

that seen for the equivalent safe cut with respect to the tau reconstruction. The

background rejection efficiencies were then read off and converted into rejection

factors which could be compared directly with those in section 5.5.2 for the safe

cuts.

In the case of the ‘real cuts’, both pT binned and global selections were produced

for each of the two variables. In the case of the relative efficiencies only pT binned

values were produced.

5.7.3 Isolation Fraction Single Cut

The distributions used to produce the pT binned single IsolationFraction cuts for

1-Prong and 3-Prong hadronic taus are shown in figures 5.8 and 5.9 respectively.

The two figures are each divided into five sub-figures corresponding to the five pT

bins, with each sub-figure showing on the left the IsolationFraction distributions

for matched and fake taus, and on the right the good tau selection and fake tau

rejection efficiencies. The IsolationFraction distributions are normalised to unit

area. For both hadronic tau prongs, it can be seen that as the pT is increased

(moving from (a) through to (e)) the discrimination between the good and fake

taus is increased. This occurs by the signal distribution becoming narrower, with

the upper edge moving towards smaller values of the IsolationFraction. The fake

tau distribution shape remains approximately constant throughout. A potential

negative effect of this is that the selection efficiency turn on curve becomes very

131

sharp at high pT, and hence the efficiency values can become very bin dependent.

As a consequence the value will become stongly sensitive to the modeling of both

the detector and the tau itself.

Reading off the selection efficiencies and calculating the rejection factors as described

previously produced the results shown in tables 5.6 to 5.9. The cut values themselves

are shown in table 5.5. Tables 5.6 and 5.7 compare the IsolationFraction assigned

efficiencies to the safe cut efficiencies for the 1-Prong and 3-Prong cases. What

can be seen from the tables is that the IsolationFraction single cut only appears to

perform better than the safe cuts, with respect to background rejection, when the

safe cut selection efficiency is noteably looser than that of the single cut. When the

selection efficiency of the two sets of cuts is approximately equal, as for the 1-Prong

or 3-Prong loose cuts in the 45-70 GeV bin, the rejection for the safe cuts is seen to

be slightly superior. This is backed up by the equivalent efficiency results for the two

prongs shown in tables 5.8 and 5.9. Here it can be seen that the safe cuts perform

better than the IsolationFraction almost exclusively for the same signal selection

efficiency value, with the exception of the 70-100 GeV loose cuts. Furthermore, it

can be seen that for the loose selections the background rejection of the single cut

is approximately equivalent to that for the safe cuts. As the cut level is moved from

loose to medium to tight the performance of the single cut degrades when compared

to the safe cuts. In addition, the discrepancy between the two sets of rejection

figures for the medium and tight cuts increases as the pT of the bin increases.

132

isolationFraction

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-1Ev

ent

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0.005

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0.015

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Unmatched

isolationFraction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Ef

ficie

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isolationFraction

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ent

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0.03

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isolationFraction

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Effic

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isolationFraction

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ent

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isolationFraction

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(c) 45-70 GeV

isolationFraction

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ent

0

0.01

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Truth matched

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isolationFraction

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ficie

ncy

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Unmatched

(d) 70-100 GeV

isolationFraction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1Ev

ent

0

0.02

0.04

0.06

0.08

0.1

Truth matched

Unmatched

isolationFraction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Effic

ienc

y

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0.2

0.4

0.6

0.8

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Truth matched

Unmatched

(e) >100 GeV

Figure 5.8: IsolationFraction : Signal and background (fake tau) distributions and effi-

ciencies for 1-Prong taus in different pT regions

133

isolationFraction

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-1Ev

ent

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0.005

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0.015

0.02

0.025

0.03

0.035

Truth matched

Unmatched

isolationFraction

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ficie

ncy

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Truth matched

Unmatched

(a) 10-25 GeV

isolationFraction

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-1Ev

ent

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0.02

0.025

0.03

0.035

Truth matched

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isolationFraction

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Effic

ienc

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Unmatched

(b) 25-45 GeV

isolationFraction

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-1Ev

ent

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0.02

0.03

0.04

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Truth matched

Unmatched

isolationFraction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Effic

ienc

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Truth matched

Unmatched

(c) 45-70 GeV

isolationFraction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1Ev

ent

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Truth matched

Unmatched

isolationFraction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Ef

ficie

ncy

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0.2

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0.6

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1

Truth matched

Unmatched

(d) 70-100 GeV

isolationFraction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1Ev

ent

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08Truth matched

Unmatched

isolationFraction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Effic

ienc

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0.6

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Truth matched

Unmatched

(e) >100 GeV


ciencies for 3-Prong taus in different pT regions

134

pT[GeV] CutLevel1-Prong 3-Prong

Real Cut Value Equivalent Cut Value Real Cut Value Equivalent Cut Value

10-25

Loose 0.355 0.255 0.385 0.545

Medium 0.255 0.115 0.305 0.365

Tight 0.165 0.075 0.235 0.205

25-45

Loose 0.235 0.195 0.325 0.405

Medium 0.155 0.105 0.255 0.205

Tight 0.095 0.065 0.185 0.145

45-70

Loose 0.165 0.175 0.245 0.255

Medium 0.105 0.095 0.185 0.165

Tight 0.065 0.055 0.145 0.115

70-100

Loose 0.125 0.305 0.195 0.405

Medium 0.085 0.075 0.155 0.135

Tight 0.055 0.055 0.115 0.105

>100

Loose 0.105 0.495 0.165 0.175

Medium 0.065 0.055 0.125 0.145

Tight 0.045 0.035 0.095 0.075

Table 5.5: IsolationFraction pT binned cut values used to select 1-Prong and 3-Prong

hadronic taus in tt̄ events. Real cuts give pre-set signal selection efficiencies, equivalent

cut values match the signal selection efficiency to that for the calorimeter only safe cuts

135

pT[GeV] CutLevelEfficiency (Safe cuts) Efficiency (IsolFrac cut) Rejection

TauRec Before/After TauRec Before/After Safe Cuts IsolFrac Cut

10-25

Loose 0.48 0.70 2.86 1.46

Medium 0.19 0.48 7.92 2.26

Tight 0.10 0.28 14.57 4.67

25-45

Loose 0.60 0.69 5.21 2.66

Medium 0.30 0.48 15.88 5.60

Tight 0.16 0.28 26.41 12.98

45-70

Loose 0.73 0.69 6.68 5.18

Medium 0.39 0.47 24.27 11.56

Tight 0.18 0.26 42.01 21.57

70-100

Loose 0.95 0.69 1.68 8.73

Medium 0.43 0.47 32.90 15.97

Tight 0.24 0.26 44.68 25.39

>100

Loose 0.98 0.67 1.11 10.98

Medium 0.36 0.44 51.48 20.52

Tight 0.16 0.26 77.55 29.12

Table 5.6: Hadronic 1-Prong tau selection efficiency and rejection factors with respect to

reconstructed taus. Values are shown for a single cut on IsolationFraction and for the tau

calorimeter only safe cuts for tt̄ events. Real IsolationFraction cuts are shown intended to

give selection efficiencies of 70%, 50% and 30%

136



10-25

Loose 0.92 0.69 1.15 1.36

Medium 0.64 0.49 1.64 1.80

Tight 0.20 0.29 3.77 2.72

25-45

Loose 0.84 0.70 1.65 1.72

Medium 0.37 0.51 4.97 2.51

Tight 0.17 0.30 9.69 4.45

45-70

Loose 0.72 0.70 2.78 2.71

Medium 0.39 0.49 9.82 4.60

Tight 0.16 0.30 21.05 7.29

70-100

Loose 0.97 0.68 1.23 4.14

Medium 0.42 0.51 14.56 6.91

Tight 0.22 0.30 26.16 12.97

>100

Loose 0.75 0.70 8.76 5.48

Medium 0.61 0.47 13.74 10.05

Tight 0.14 0.27 62.08 16.27


reconstructed taus. Values are shown for a single cut on IsolationFraction and for the tau

calorimeter only safe cuts for tt̄ events. Real IsolationFraction cuts are shown intended to

give selection efficiencies of 70%, 50% and 30%

137



10-25

Loose 0.48 0.48 2.86 2.26

Medium 0.19 0.18 7.92 8.39

Tight 0.10 0.11 14.57 13.74

25-45

Loose 0.60 0.59 5.21 3.67

Medium 0.30 0.31 15.88 11.09

Tight 0.16 0.17 26.41 20.32

45-70

Loose 0.73 0.72 6.68 4.60

Medium 0.39 0.42 24.27 13.60

Tight 0.18 0.20 42.01 25.21

70-100

Loose 0.95 0.95 1.68 1.77

Medium 0.43 0.40 32.90 18.82

Tight 0.24 0.26 44.68 25.39

>100

Loose 0.98 0.98 1.11 1.11

Medium 0.36 0.35 51.48 24.49

Tight 0.16 0.17 77.55 35.37


reconstructed taus. Values are shown for a single cut on IsolationFraction and for the

tau calorimeter only safe cuts for tt̄ events with the IsolationFraction selection efficiencies

matched to those of the equivalent safe cuts

138



10-25

Loose 0.92 0.92 1.15 1.07

Medium 0.64 0.64 1.64 1.44

Tight 0.20 0.21 3.77 3.44

25-45

Loose 0.84 0.85 1.65 1.32

Medium 0.37 0.36 4.97 3.68

Tight 0.17 0.19 9.69 7.28

45-70

Loose 0.72 0.74 2.78 2.51

Medium 0.39 0.40 9.82 5.67

Tight 0.16 0.17 21.05 11.01

70-100

Loose 0.97 0.97 1.23 1.26

Medium 0.42 0.42 14.56 9.32

Tight 0.22 0.22 26.16 15.15

>100

Loose 0.75 0.74 8.76 4.88

Medium 0.61 0.60 13.74 7.50

Tight 0.14 0.13 62.08 22.80


reconstructed taus. Values are shown for a single cut on IsolationFraction and for the

tau calorimeter only safe cuts for tt̄ events with the IsolationFraction selection efficiencies

matched to those of the equivalent safe cuts

139

Global Pt Cut

Having noted that the performance of a pT binned single cut is in general worse, and

at best equivalent to, the safe cuts, the global 1-Prong and 3-Prong IsolationFraction

cuts were also produced. The advantage of producing a global cut of this nature is

that the performance of the cut will vary more smoothly with pT than will be the

case for a discretely binned set of cuts. Figure 5.10 shows the IsolationFraction and

corresponding efficiency distributions for the 1-Prong (a) and 3-Prong (b) hadronic

taus. The resulting assigned signal selection efficiencies and background rejection

factors are shown in table 5.10 for both 1-Prong and 3-Prong taus. Looking at

table 5.6 for the 1-Prong case binned cut values and at table 5.7 for the 3-Prong

case it can be seen that the global pT cut is seen to offer a rejection value on a par

with the binned cut for the 25-45 GeV region. At higher pT, the global pT cut is

looser than the binned cuts, and so as a consequence the rejection is less powerful

for the global cut (although the efficiency would also be expecter to be higher).

140

isolationFraction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1Ev

ent

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Truth matched

Unmatched

isolationFraction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Effic

ienc

y

0

0.2

0.4

0.6

0.8

1

Truth matched

Unmatched

(a) 1-Prong

isolationFraction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1Ev

ent

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035 Truth matched

Unmatched

isolationFraction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Effic

ienc

y

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0.4

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1

Truth matched

Unmatched

(b) 3-Prong


ciencies for hadronic taus over the entire pT range

Decay type Cut Level Cut ValueEfficiency (IsolFrac) IsolFrac

TauRec Before/After Rejection

1-Prong

Loose 0.235 0.71 2.44

Medium 0.145 0.51 5.06

Tight 0.085 0.30 9.29

3-Prong

Loose 0.295 0.69 1.84

Medium 0.215 0.49 2.92

Tight 0.155 0.29 4.82

Table 5.10: Hadronic tau selection efficiency and rejection factors with respect to recon-

structed taus. Values are shown for a single cut on IsolationFraction for tt̄ events. Single

cuts are produced for one bin covering the whole tau pT range

141

5.7.4 IsolationFraction Summary

It has been seen that for a single cut on the IsolationFraction of the tau, the dis-

crimination power for distinguishing good taus from fakes increases as pT increases.

Although it is difficult to make an exact comparison between the pT binned Iso-

lationFraction cut and the calorimeter only safe cuts due to the variation in the

selection efficiencies of the latter, it has been seen that the safe cuts generally give

better rejection for equivalent efficiency values. The IsolationFraction single cut was

seen to perform better only when the safe cut efficiency is excessively large (relative

to the target efficiency). An IsolationFraction pT a global pT cut (in general) was

seen to give a performance akin to that for the binned single variable cut in the

25-45 GeV pT region.

5.7.5 EmRadius Single Cut

It was seen in 5.7.3 that in general a single cut, either pT dependent or for global pT,

on the IsolationFraction does not give better hadronic tau identification than the

four variable calorimeter only safe cuts. However, although IsolationFraction can

be considered the simplest of the four safe cut variables, EmRadius is potentially

the better discriminant. Therefore the process followed in 5.7.3 was repeated to

examine a single cut on the EmRadius. The pT binned EmRadius good and fake

tau distributions for tt̄ events, together with their equivalent signal selection and

background rejection efficiencies, are shown by figures 5.11 and 5.12 for the 1-Prong

and 3-Prong hadronic taus respectively. As for IsolationFraction, the figures show

142

that the distinction between the taus well matched to the Monte Carlo truth and

the fakes improves with increasing pT. Likewise, as for IsolationFraction the signal

selection efficiency turn-on curve becomes steep at high pT. This is again the case for

both prongs. As before, the background rejection factors were calculated for assigned

signal selection efficiencies, with respect to reconstructed taus, of 70%, 50% and 30%.

These are compared to the safe cuts in tables 5.12 and 5.13 with the cut values shown

in table 5.11. It is difficult to make a direct comparison with the safe cuts for the

EmRadius assigned efficiencies due to variance of the safe cut signal efficiencies,

but where they are similar in the 3-Prong 45-70 GeV loose case, the EmRadius cut

performs better than the safe cuts. However, the EmRadius assigned efficiencies

can be compared directly to the IsolationFraction assigned efficiencies in tables 5.6

and 5.7. Making this direct comparison of the two single variable pT binned cuts,

it can be seen that the EmRadius cut performs better in almost every case except

the tight 1-Prong 10-25 GeV cut, where the rejection for the two variables is almost

identical. The advantage of using the EmRadius cut over the IsolationFraction cut

also becomes more beneficial with increasing pT. This conclusively supported the

hypothesis that EmRadius is a better good tau distinguishing variable for tt̄ events.

Furthermore, it suggested that EmRadius would perform better in an equivalent

efficiency comparison with the safe cuts.

To allow better examination of the performance, equivalent EmRadius efficiencies

were again produced and are shown in tables 5.14 and 5.15. The cuts themselves

are again shown in table 5.11. From examining these, it can be seen that for all cut

levels, in all pT bins, and for both prongs the EmRadius single cuts perform as well

143

or better than the safe cuts with regards to background rejection for an equivalent

good tau selection efficiency. Consequently, it is possible to conclude that it is

possible to produce a hadronic tau selection that for tt̄ events performs as well as

the calorimeter only safe cuts, using only the variable EmRadius for calorimeter

seeded tau candidates.

144

emRadius

0 0.05 0.1 0.15 0.2 0.25 0.3

-1Ev

ent

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0.005

0.01

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0.02

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0.03Truth matched

Unmatched

emRadius

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ficie

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(a) 10-25 GeV

emRadius

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-1Ev

ent

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0.02

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0.03

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Unmatched

emRadius

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Effic

ienc

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(b) 25-45 GeV

emRadius

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ent

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emRadius

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Effic

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(c) 45-70 GeV

emRadius

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emRadius

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(d) 70-100 GeV

emRadius

0 0.05 0.1 0.15 0.2 0.25 0.3

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ent

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0.1

Truth matched

Unmatched

emRadius

0 0.05 0.1 0.15 0.2 0.25 0.3

Effic

ienc

y

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0.2

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Truth matched

Unmatched

(e) >100 GeV

Figure 5.11: EmRadius : Signal and background (fake tau) distributions and efficiencies

for 1-Prong taus in different pT regions

145

emRadius

0 0.05 0.1 0.15 0.2 0.25 0.3

-1Ev

ent

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035 Truth matched

Unmatched

emRadius

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ficie

ncy

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Truth matched

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(a) 10-25 GeV

emRadius

0 0.05 0.1 0.15 0.2 0.25 0.3

-1Ev

ent

0

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0.01

0.015

0.02

0.025

0.03

0.035

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0.045

Truth matched

Unmatched

emRadius

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Effic

ienc

y

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Truth matched

Unmatched

(b) 25-45 GeV

emRadius

0 0.05 0.1 0.15 0.2 0.25 0.3

-1Ev

ent

0

0.01

0.02

0.03

0.04

0.05Truth matched

Unmatched

emRadius

0 0.05 0.1 0.15 0.2 0.25 0.3

Effic

ienc

y

0

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1

Truth matched

Unmatched

(c) 45-70 GeV

emRadius

0 0.05 0.1 0.15 0.2 0.25 0.3

-1Ev

ent

0

0.01

0.02

0.03

0.04

0.05

0.06

Truth matched

Unmatched

emRadius

0 0.05 0.1 0.15 0.2 0.25 0.3Ef

ficie

ncy

0

0.2

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Truth matched

Unmatched

(d) 70-100 GeV

emRadius

0 0.05 0.1 0.15 0.2 0.25 0.3

-1Ev

ent

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07 Truth matched

Unmatched

emRadius

0 0.05 0.1 0.15 0.2 0.25 0.3

Effic

ienc

y

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0.2

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Truth matched

Unmatched

(e) >100 GeV


for 3-Prong taus in different pT regions

146

pT[GeV] CutLevel1-Prong 3-Prong

Real Cut Value Equivalent Cut Value Real Cut Value Equivalent Cut Value

10-25

Loose 0.1377 0.1105 0.1547 0.2057

Medium 0.1139 0.0731 0.1309 0.1479

Tight 0.0901 0.0561 0.1105 0.0969

25-45

Loose 0.1037 0.0901 0.1207 0.1479

Medium 0.0799 0.0595 0.1003 0.0901

Tight 0.0595 0.0459 0.0833 0.0697

45-70

Loose 0.0765 0.0833 0.1003 0.1003

Medium 0.0595 0.0527 0.0799 0.0697

Tight 0.0459 0.0391 0.0663 0.0527

70-100

Loose 0.0629 0.1445 0.0833 0.1853

Medium 0.0493 0.0459 0.0663 0.0595

Tight 0.0391 0.0357 0.0527 0.0493

>100

Loose 0.05270 0.2159 0.0697 0.0731

Medium 0.0391 0.0357 0.0561 0.0629

Tight 0.0323 0.0289 0.0459 0.0391

Table 5.11: EmRadius pT binned cut values used to select 1-Prong and 3-Prong hadronic

taus in tt̄ events. Real cuts give pre-set signal selection efficiencies, equivalent cut values

match the signal selection efficiency to that for the calorimeter only safe cuts

147

pT[GeV] CutLevelEfficiency (Safe cuts) Efficiency (EmRadius cut) Rejection

TauRec Before/After TauRec Before/After Safe Cuts EmRadius Cut

10-25

Loose 0.48 0.69 2.86 1.89

Medium 0.19 0.51 7.92 2.7

Tight 0.10 0.32 14.57 4.63

25-45

Loose 0.60 0.70 5.21 3.37

Medium 0.3 0.52 15.88 6.84

Tight 0.16 0.30 26.41 15.62

45-70

Loose 0.73 0.68 6.68 8.22

Medium 0.39 0.50 24.27 17.23

Tight 0.18 0.29 42.01 31.81

70-100

Loose 0.95 0.69 1.68 13.95

Medium 0.43 0.50 32.90 26.15

Tight 0.24 0.30 44.68 42.80

>100

Loose 0.98 0.69 1.11 22.35

Medium 0.36 0.46 51.48 42.20

Tight 0.16 0.27 77.55 59.84

Table 5.12: Hadronic 1-Prong tau selection efficiency and rejection factors with respect

to reconstructed taus. Values are shown for a single cut on EmRadius and for the tau

calorimeter only safe cuts for tt̄ events. Real EmRadius cuts are shown intended to give

selection efficiencies of 70%, 50% and 30%

148



10-25

Loose 0.92 0.69 1.15 1.60

Medium 0.64 0.49 1.64 2.07

Tight 0.20 0.31 3.77 2.86

25-45

Loose 0.84 0.69 1.65 2.43

Medium 0.37 0.50 4.97 3.77

Tight 0.17 0.30 9.69 6.12

45-70

Loose 0.72 0.71 2.78 3.81

Medium 0.39 0.50 9.82 6.87

Tight 0.16 0.32 21.05 11.36

70-100

Loose 0.97 0.71 1.23 6.43

Medium 0.42 0.51 14.56 12.52

Tight 0.22 0.29 26.16 26.41

>100

Loose 0.75 0.70 8.76 10.72

Medium 0.61 0.51 13.74 19.35

Tight 0.14 0.30 62.08 38.92



calorimeter only safe cuts for tt̄ events. Real EmRadius cuts are shown intended to give

selection efficiencies of 70%, 50% and 30%

149



10-25

Loose 0.48 0.48 2.86 2.88

Medium 0.19 0.20 7.92 8.01

Tight 0.10 0.10 14.57 14.49

25-45

Loose 0.60 0.61 5.21 4.85

Medium 0.30 0.30 15.88 15.62

Tight 0.16 0.15 26.41 27.08

45-70

Loose 0.73 0.74 6.68 6.28

Medium 0.39 0.41 24.27 23.37

Tight 0.18 0.19 42.01 40.98

70-100

Loose 0.95 0.95 1.68 1.79

Medium 0.43 0.43 32.90 31.40

Tight 0.24 0.22 44.68 50.26

>100

Loose 0.98 0.98 1.11 1.14

Medium 0.36 0.37 51.48 48.69

Tight 0.16 0.17 77.55 78.09



calorimeter only safe cuts for tt̄ events with the EmRadius selection efficiencies matched

to those of the equivalent safe cut

150



10-25

Loose 0.92 0.92 1.15 1.18

Medium 0.64 0.63 1.64 1.69

Tight 0.20 0.20 3.77 3.85

25-45

Loose 0.84 0.85 1.65 1.69

Medium 0.37 0.38 4.97 5.01

Tight 0.17 0.17 9.69 10.09

45-70

Loose 0.72 0.71 2.78 3.81

Medium 0.39 0.37 9.82 9.97

Tight 0.16 0.14 21.05 20.32

70-100

Loose 0.97 0.97 1.23 1.3

Medium 0.42 0.40 14.56 18.54

Tight 0.22 0.23 26.16 31.52

>100

Loose 0.75 0.74 8.76 9.29

Medium 0.61 0.64 13.74 14.49

Tight 0.14 0.17 62.08 53.29



calorimeter only safe cuts for tt̄ events with the EmRadius selection efficiencies matched

to those of the equivalent safe cut

151

Global Pt Cut

Following the same procedure as for IsolationFraction, a global pT EmRadius single

variable selection was evaluated. Fig. 5.13 shows the EmRadius distributions and

efficiency curves for the 1-Prong (a) and 3-Prong (b) taus, while the background

rejection factors for the assigned signal selection efficiencies are given in table 5.16.

These can then be compared back to the pT binned EmRadius rejection factors in

tables 5.12 and 5.13. As for IsolationFraction, the global pT cut provides a rejection

akin to that of the pT binned cut for the 25-45 GeV region, with the global cut

being looser at larger pT. Noting that the shape of the background distribution is

similar for each of the pT bins but that the signal shape changes, it is possible to

see how tightening the cut via the use of a pT binned selection can provide a better

rejection at higher pT. This applies for both hadronic tau prongs. Comparing back

to the IsolationFraction global cut in table 5.10 the global EmRadius cut is seen to

perform significantly better.

5.8 Overall Conclusions

Within this chapter a general introduction was given on tau identification with

the ATLAS detector. The calorimeter only tau safe cuts were introduced and an

investigation was carried out to compare their performance for tt̄ events to that for

a combined sample of Z → ττ and bbA → bbττ events. It was concluded that with

regards to good tau selection efficiencies the safe cut performance compared well

152

emRadius

0 0.05 0.1 0.15 0.2 0.25 0.3

-1Ev

ent

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04 Truth matched

Unmatched

emRadius

0 0.05 0.1 0.15 0.2 0.25 0.3

Effic

ienc

y

0

0.2

0.4

0.6

0.8

1

Truth matched

Unmatched

(a) 1-Prong

emRadius

0 0.05 0.1 0.15 0.2 0.25 0.3

-1Ev

ent

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Truth matched

Unmatched

emRadius

0 0.05 0.1 0.15 0.2 0.25 0.3

Effic

ienc

y

0

0.2

0.4

0.6

0.8

1

Truth matched

Unmatched

(b) 3-Prong


for hadronic taus over the entire pT range

Decay type Cut Level Cut ValueEfficiency (EmRadius) EmRadius

TauRec Before/After Rejection

1-Prong

Loose 0.1037 0.70 3.03

Medium 0.0731 0.51 6.49

Tight 0.0527 0.32 11.63

3-Prong

Loose 0.1207 0.69 2.22

Medium 0.0935 0.50 3.63

Tight 0.0731 0.31 6.11

Table 5.16: Hadronic tau selection efficiency and rejection factors with respect to recon-

structed taus. Values are shown for a single cut on EmRadius for tt̄ events. Single cuts

are produced in one bin for the whole tau pT range

153

in top events relative to the cleaner sample, behaving in the same way but with a

slightly lower efficiency. Two alternative selections were proposed based on a single

variable only, and it was concluded that for the same pT binning as the safe cuts,

an equivalent performance could be obtained using a single cut on the EmRadius.

A global pT selection was also studied and seen to perform in a similar way to a pT

binned selection in the pT range of 25-45 GeV. 4

4Since this study was completed, a new safe tau selection has been produced by the ATLAS

tau working group [55]. The new selection uses only 3 variables (of which EmRadius is the main

discriminant) and two pT bins covering 0-100 GeV and >100 GeV respectively.

154

Chapter 6

Measurement of the tt̄ Cross

Section

6.1 Introduction

Described in this chapter is a proposed method for measuring the tt̄ production cross

section at the LHC, via the tau+jets channel with the ATLAS detector. Intended for

use with early LHC data, the analysis is based on a series of simple cuts. These were

designed to suppress the various standard model backgrounds whilst simultaneously

increasing the purity of the desired section of the tt̄ signal. The analysis has been

largely developed with Monte Carlo simulated events, with a first look being made

at the 2010 ATLAS data.

155

6.2 Signal

At the LHC tt̄ pairs are produced readily. The events are classified by the top decay

products as described in 1.5. Excluding the fully hadronic tt̄ events, these were simu-

lated for a centre-of-mass energy of 7 TeV, at next to leading order (NLO), using the

MC@NLO v3.41 event generator [56] coupled to Herwig/Jimmy to provide the par-

ton shower modelling [56]. A top mass of 172.5 GeV was assumed and the CTEQ66

NLO pdf set used [56]. The sample was simulated with a cross-section of 80.201 pb

for the non-hadronic tt̄ and then scaled to a more recent theoretical prediction by

Ulrich Husemann (Moch and Uwer) [57] by use of a ‘K-factor’of 1.11 [58].

6.3 Backgrounds

For the purposes of the analysis described, the fully hadronic tt̄ decay (not includ-

ing taus) is considered as part of the background. This was also simulated using

Mc@NLO and Herwig/Jimmy with a cross-section of 64.064 pb corrected by a K

factor of 1.17 [58]. The same pdf set was also used as for the signal sample. Single

top samples contribute a small background and were generated with Mc@NLO cou-

pled to Herwig to provide the parton showering [58]. Cross-sections for the single

top samples were taken directly from the generator at NLO [58].

The primary backgrounds for top studies are provided by W/Z + jets (both light

quark and heavy flavour) and QCD events. The primary background varies de-

pending on the particular top decay being studied. For tau+lepton events, the

156

W/Z+jets are more significant, whereas controlling the QCD background is the key

factor for studies in the tau+jets scenario. For W/Z+jets a series of different Monte

Carlo samples was generated with Alpgen [58] with the parton shower modeled by

Herwig/Jimmy [58]. A pdf set based on CTEQ6L1 was used. The samples were

generated in the form W+Np(i) and Z+Np(i) where i corresponds to the number

of additional partons produced in association to the W boson. Samples were sepa-

rately produced for the W or Z decaying to each of the lepton flavours. Likewise,

similar samples were produced of the form W/Z+b̄+Np(i) which have a smaller

cross-section but final state closer to the tt̄ signal. As for the different top samples

K factors were used to rescale the cross sections.

QCD multijet samples were generated with Alpgen, again using Herwig/Jimmy to

provide the parton shower modelling [58]. Samples were split up into a series of

pT slices and based on the number of additional initial partons in the scatter. A

separate set of samples of the same type were produced in the same way with the

addition of a b̄ pair. K factors were not used for the QCD samples. In addition,

the very large cross sections present for the low pT and low parton cases meant

that it was not possible to simulate a number of events of similar magnitude to

that expected in the data. Whilst scale factors were used to get an idea of the

QCD contribution, ideally the QCD background should be evaluated by data driven

techniques. From the Monte Carlo, a second estimate of the QCD contribution was

obtained by examining an inclusive dijet sample generated by and with the parton

shower provided by Pythia [40]. This was divided into nine pT slices labeled J0

to J9, with large scale factors again required for the lowest. The sample binning

157

was classified acording to the pT of the hard scatter, with the ranges defined; J0 =

10-17 GeV, J1 = 17-35 GeV, J2 = 35-70 GeV, J3 = 70-140 GeV, J4 = 140-280 GeV,

J5 = 280-560 GeV, J6 = 560-1120 GeV, J7 = 1120-2280 GeVand J8 = 2280 GeVand

above [59]. As better statistics were available for the Pythia samples, these were used

in preference to the Alpgen samples to estimate the regions of phase space expected

to be occupied by QCD events after a given selection was applied. However, due

to both statistics and uncertainties in the cross-sections [58], it was necessary to

estimate the true shape and normalisation of the QCD events from data.

6.4 LHC Data Periods

During 2010 the ATLAS detector collected a nominal 45.0 pb−1 of proton-proton

physics data [21]. These data were divided into nine main luminosity periods labeled

A-I [60]. The bulk of the data were collected in the last two of these periods, with

periods H and I together comprising a nominal 32.3 pb−1 [60]. It is this sample

that was examined by the analysis described in this chapter. Data during these two

periods were output into four inclusive data streams; egamma, jetTauEtMiss, muon

and minBias [61]. For the purpose of this analysis the jetTauEtMiss stream was

used, with checks for good data applied via the appropriate ‘good run lists’ (GRL)

for periods H 1 and I 2 respectively [62]. After application of the GRL the total

1data10 7TeV.periodH.166466-166964 LBSUMM DetStatus-v03-pass1-analysis-

2010H top allchannels 7TeV.xml2data10 7TeV.periodI.167575-167844 LBSUMM DetStatus-v03-pass1-analysis-

2010I top allchannels 7TeV.xml

158

luminosity processed by the analysis was 26.4 pb−1 [63].

6.5 Object Pre - Selections

6.5.1 Tau

The good tau selection used was based on the EmRadius single variable, global pT,

cut described in 5.7.5. Tau candidates were however required to be both calorimeter

and track seeded. This was then developed in a way consistent with the electron

and muon selections used by the ATLAS top physics group. As such, selected tau

candidates were required to pass the tight cut level (by possessing an EmRadius

< 0.05 for the 1-Prong case and < 0.07 in the three prong case, where the prong

was defined in terms of the number of reconstructed tracks. 1-Prong candidates

were required to have exactly one track and 3-Prong greater than or equal to two

tracks), have offline pT > 20 GeV and satisfy |η| <2.5 (so as to lie within the real

calorimeter coverage). To improve the discrimination between genuine taus and fakes

with a narrow jet topography, candidates were required to have exactly one or three

reconstructed tracks. Fig 6.1 shows the number of tracks for candidates which are

matched to 1-Prong and 3-Prong hadronic taus in the signal sample, compared to the

non-matched candidates. Similarly, it was required that the charge of the selected

candidates be ±1, with Fig. 6.2 showing the charge of truth matched and non truth

matched candidates in the Monte Carlo signal sample. Finally, the calorimeter crack

region that was excluded from the selected electrons was also excluded from the tau

159

selection (see section 6.5.6). Any tau candidate found within 1.37 < |η| < 1.52 was

therefore discarded. This was to prevent any electrons produced in an event but

going into the crack region from being incorrectly reconstructed as tau candidates

and not removed by overlap removal. As discussed previously 5.2, the good tau

selection was only intended to identify hadronic decaying taus. Any taus which

decayed directly to either electrons or muons were considered as such.

Number of Tracks0 1 2 3 4 5 6 7 8 9 10

-1Ev

ent

0

0.2

0.4

0.6

0.8

1Truth matched

Unmatched

Figure 6.1: Number of tracks associated with reconstructed tau candidates when either

matched to a Monte Carlo truth hadronic tau or not. Plots are normalised to unit area

6.5.2 Jet

Jets were reconstructed via the Anti-k⊥ algorithm for a D size parameter of 0.4 [64]

and calibrated in accordance with the H1 calibration at the hadronic scale [56].

These were built from uncalibrated calorimeter topological clusters at the EM scale [56].

Topological clustering is the current ATLAS default strategy which sums neighbour-

160

Tau charge-4 -3 -2 -1 0 1 2 3 4

-1Ev

ent

0

0.2

0.4

0.6

0.8

1Truth matched

Umatched

Figure 6.2: Charge of reconstructed tau candidates when either matched to a Monte Carlo

truth hadronic tau or not. Plots are normalised to unit area

ing calorimeter cells based on their energy significance to build up the cluster, which

can be of varying size [65]. This contrasts to the alternative algorithm (formerly the

ATLAS default when used with calorimeter towers as an input) which used a fixed

size cone in η×φ . Jets were required to have an offline pT > 20 GeV (minimum jet

pT was set at this stage to allow overlap removal as per 6.5.6). It was also required

that any jets lie within the combined ATLAS calorimeter and inner tracker coverage

of |η| < 2.5. This was necessary to allow the use of B-tagging, while tt̄ events are

also typically produced at central values of η.

6.5.3 Missing Et

Missing ET in each event was calculated via the MET RefFinal method (which uses

a refined calibration). This takes input cells, associates them with reconstructed

161

objects (which are ordered electron, photon, hadronic tau, jet and muon) and then

replaces the original cell calibration with that from the relevant reconstructed object

(which is considered to be better known [66]). Cells are only associated with the

first valid reconstructed object (if they contribute to several different objects) so

as to prevent overlaps in the missing ET calculation. The calculation carries out

separate sums for the Ex and Ey components of the total missing ET, with all cells

being included. Any cells which do not form part of any reconstructed object have

a global calibration applied. A 20 GeV base missing ET cut was required.

6.5.4 Electron

Electrons are reconstructed in ATLAS events via three different algorithms. ‘Stan-

dard electrons’ are produced via a cluster based algorithm used to identify high

energy isolated electrons in the EM calorimeter [67]. ‘Soft electrons’ are produced

by an algorithm, seeded from an inner detector track, intended to identify either

low energy electrons or electrons originating from a hadron jet. The third algorithm

focuses on identifying electrons produced in the forward region of the detector. For

the purposes of the selection applied here, electron candidates were required to origi-

nate from either the standard or soft algorithm. Candidates were required to possess

an offline pT > 20 GeV and lie within |η| < 2.5 but not in the calorimeter crack

region of 1.37 < |η| < 1.52. In addition, they were required to pass the medium level

‘isEM’ quality cuts comprising a series of calorimeter isolation and shower shape cuts

together with limited tracking constraints. Finally, a futher isolation requirement

162

was added by requiring the etcone20 (total ET contained within a cone of ∆R <0.2

around the cluster [56]) variable to have a value > 4 + 0.023×(candidate offline pT),

while the track matched to the calorimeter cluster was required to have a value for

E/pT of the correct size for an electron plus a hit in the B-layer (first layer of the

tracker pixels where the track should cross an active detector).

6.5.5 Muon

A number of different muon reconstruction algorithms are available within ATLAS

which are split into two groups. These are ‘standalone’ muons which only use in-

formation from the muon spectrometer, and ‘combined’ muons which use the muon

spectrometer in association with the inner detectors. Here ‘MuID’ (Muon IDentifica-

tion) muons were taken as the starting point, which combine the muon spectrometer

tracks with inner detector tracks and calorimeter deposits. Selected muons (with

author of 12) were required to pass the tight quality cuts, whilst possessing an offline

pT > 20 GeV and |η| < 2.5. In addition, two futher isolation constraints were applied

by requiring the variables Ptcone30 (total track pT in a cone of ∆R <0.3 around

the muon candidate excluding the muon track) and Etcone30 (total calorimeter ET

in a cone of ∆R <0.3 around the muon candidate) to be smaller than 4 GeV.

163

6.5.6 Overlap Removal

Each aspect of the ATLAS reconstruction considers the detector signatures indepen-

dently. Consequently, providing the relevant constraints are passed, a particular set

of signatures in the detector could be simultaneously reconstructed as (for example)

an electron, tau and jet. To avoid double counting, a process of overlap removal

was carried out. For electrons-jet and muon-jet overlaps the same procedure was

followed as per [56] with removal based on spatial matching. Any selected jet located

within 4R<0.2 of a selected electron was removed. Likewise, any selected muon lo-

cated withing 4R<0.4 of a selected jet was then also removed. In addition, further

overlaps were processed with respect to the selected taus. Any selected tau found

within 4R<0.2 of a remaining selected electron was removed. Then any remaining

selected jet within 4R<0.4 of the remaining good taus was removed. Finally, any

muons remaining within 4R<0.4 of a selected tau were removed.

6.6 Event Selections

6.6.1 Choice of tt̄ channel

As discussed in 1.5 tt̄ events are characterised by the decay of the W -bosons coming

from the two top quarks. Consequently there are three different classes of tt̄ events

featuring taus:

• Tau + jets : One of the W-bosons decays to a hadronic tau and the sec-

164

ond decays to a quark pair. The event is characterised by the presence of a

hadronic tau, four jets (of which two are b-jets) and significant missing ET as

a consequence of the neutrino produced in the tau decay.

• Tau + lepton : One W-boson decays to a hadronic tau with the second de-

caying to either an electron or a muon. As such the event signature comprises

a hadronic tau, single high energy lepton, two b-jets and missing ET arising

from the neutrinos produced in both W decays.

• Two tau events : Both W-bosons decay to hadronic taus. Two b-jets are also

produced and large missing ET observed.

It should be noted that for the purposes of this analysis a tau was interpreted as

the hadronically decaying cases only. Taus decaying to leptons were lumped in

with the standard leptonic modes as they are virtually indistinguishable from an

experimental viewpoint.

Of the three event topologies, the tau + jets and tau + lepton cases are the most

useful. Both have positive and negative points associated with them. The tau + jets

channel has the advantage that one of the top quarks in the tt̄ pair decays hadron-

ically and so can be fully reconstructed. This has the advantage that plotting the

invariant mass of the hadronic top provides a method of verifying whether selected

events do indeed come from a tt̄ pair. However, the signature for this channel com-

prises a hadronic tau, four hadron jets and missing ET. Consequently, it would

be expected to suffer badly from QCD backgrounds in the enviroment of a proton

collider. Considering the tau + lepton channel, the situations are largely reversed.

165

In this case a hard lepton is produced in the event, which both allows for easy trig-

gering and also acts as a powerful supression against QCD. However, neither of the

top quarks can be fully reconstructed, thereby making it more difficult to verify the

tt̄ content of any events passing a given selection. Furthermore, the tau + lepton

channel is known to suffer a significant cross talk background from the other decay

channels of the tt̄ pair which is difficult to remove [68]. Table 6.1 shows the number

of events which pass basic preselections for tau + jets and tau + lepton channels

when a small test study was carried out for 1000 tt̄ events. For the former the

selection to be described in 6.6.2 was used whereas for the latter exactly one good

selected tau and lepton were required, together with two good jets and missing ET

greater than 20 GeV. As can be seen, for the tau + lepton selection the signal only

makes up 20% of the events passing.

Channel Events passing (tau + jets selection) Events passing (tau + lepton selection)

Tau + jets 380 33

Tau + lepton 21 124

Double tau 6 7

Lepton + jets 265 513

Dilepton 7 74

S/B 1.27 0.2

Table 6.1: Comparison of the number of events in different tt̄ signal channels passing

preselections for tau + jets and tau + lepton events

Two tau events suffer the same disadvantages as both of the other two channels in

that they do not contain a lepton for QCD supression and neither top quark can be

fully reconstructed.

166

The remainder of this chapter describes a technique developed to allow a measure-

ment of the tt̄ cross section from the tau + jets channel, including an estimate of

the QCD background to the channel from data. The analysis was deliberately de-

veloped to use simple cuts which were considered to be safe in the early ATLAS

data. Multivariant techniques were therefore deliberately avoided.

6.6.2 Tau + Jets Channel Preselection

As described above, the tau + jets channel in the decay of a tt̄ decay is characterised

by the presence of a hadronically decaying tau lepton, two jets originating from b

quarks, two light quark jets (plus any additional jets produced by gluon radiation)

and a degree of missing ET due to the presence of neutrinos associated with the

W → τ decay. An initial event preselection was therefore introduced, in addition to

the object selections already described, to discard any events which did not fit in to

the expected tau + jets topology. The cuts applied were as follows:

• Require exactly one good 1-Prong tau, passing the tight hadronic tau selection

and with pT >20 GeV.

• Veto any event containing either a good electron or good muon (as described

in the object selections) with pT >20 GeV.

• Demand at least four good jets with pT >20 GeV, of which at least three

possess pT >40 GeV.

• Require a minimum of 20 GeV missing ET.

167

While the base pre-selection alone removes a large proportion of the non top-like

backgrounds, such as low multiplicity QCD and W/Z+jets events where the W

bosons decay to real leptons within coverage, several further cuts are required to aid

isolation of the signal channel.

6.6.3 Missing ET and event scalar ET

Two techniques which can be used to further suppress background from QCD mul-

tijet processes are by raising the cut on the event missing ET and by cutting on the

total scalar ET of the event.

In a pure QCD process, energetic neutrinos are not expected to be produced. As a

consequence, it would not be expected for large amounts of missing ET to feature

in such events. Fig. 6.3 shows missing ET plotted versus three jet mass (for the

combination with the highest combined pT, see 6.7.1 for details) for the Monte Carlo

tt̄ dataset and the Pythia QCD samples. Requiring missing ET > 50 GeV cuts out

a significant portion of the tt̄ signal, but almost entirely removes the remaining low

energy QCD events from the region where cross sections are expected to be large.

The total scalar ET of each event was formed by summing the individual ET’s of

the selected tau candidate with that of the four highest pT jets and the missing ET.

It can be seen from Fig. 6.4 how putting an upper cut on the total scalar ET at

500 GeV controls the high energy part of the QCD spectrum without significantly

cutting into the tt̄ signal region.

168

Combining the two variables, candidate events were required to have missing ET >

50 GeV and an event scalar ET < 500 GeV.

) [MeV]T

(Largest PjjjM0 100 200 300 400 500 600 700 800

310×

[MeV

]M

issTE

0

50

100

150

200

250310×

-310

-210

-110

(a) tt̄

) [MeV]T

(Largest PjjjM0 100 200 300 400 500 600 700 800

310×

[MeV

]M

issTE

0

50

100

150

200

250310×

1

10

210

(b) Pythia QCD

Figure 6.3: Correlation between the missing ET and the three jet mass mjjj with the

highest combined pT for Monte Carlo tt̄ events and Pythia QCD samples. Plots are

normalised to 26.4 pb−1

[MeV]TScalar E0 100 200 300 400 500 600 700 800

310×

[MeV

]M

issTE

0

50

100

150

200

250310×

-310

-210

-110

(a) tt̄

[MeV]TScalar E0 100 200 300 400 500 600 700 800

310×

[MeV

]M

issTE

0

50

100

150

200

250310×

1

10

210

(b) Pythia QCD

Figure 6.4: Correlation between the missing ET and the event scalar ET for Monte Carlo

tt̄ events and Pythia QCD samples. Plots are normalised to 26.4 pb−1

169

6.6.4 Transverse Mass Cut

It is possible to calculate the transverse mass of the tau candidate and the event

missing ET via;

mT =√

(Eτ + ETmiss)

2 − ((pxτ+ Ex

miss)2 + (pyτ

+ Eymiss)

2). (6.1)

The main purpose of calculating the transverse mass was to provide a means of

reducing the self contamination of the tau + jets channel from the other decay modes

of the tt̄ pair. Fig. 6.5 illustrates the transverse mass plotted for the tau + jets case

when compared to the other decays of the top pair which pass the preselection. In

the case of the tau + jets channel the distribution is roughly constant from zero

up to around 70 GeV and then falls away for values above this. In contrast, for

the semileptonic decays with no truth taus present in the decay (and also to a less

extreme degree for the dileptonic decays), the distribution is seen to be strongly

peaked at around 80 GeV. Consequently, it was required that events should have

a transverse mass for the tau and missing ET < 60 GeV. Whilst this increases the

signal purity, it also helps to remove any other background where the transverse

mass of the missing ET and the tau candidate should fall above the cut value.

6.6.5 B Tagging

ATLAS makes use of a variety of algorithms designed to identify hadronic jets

originating from or containing b quarks/mesons. Of these methods the so called

‘SV0’ tagger uses the long lifetime of b-quark to search for b-jets. B-quark lifetimes

170

[MeV]TM0 50 100 150 200 250

310×

-1Ev

ent

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

[MeV]TM0 50 100 150 200 250

310×

-1Ev

ent

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07 - 1 tautDL t - 2 tautDL t - 1 tautSL t - No tautDL t - No tautSL t

- 1 tautDL t - 2 tautDL t - 1 tautSL t - No tautDL t - No tautSL t

(a)

[MeV]TM0 50 100 150 200 250

310×

-1Ev

ent

0

0.02

0.04

0.06

0.08

0.1 - 1 tautSL t

- No tautt

(b)

Figure 6.5: Transverse mass of the tau and missing ET in non-hadronic Monte Carlo tt̄

events. Shown in 6.5(a) is a breakdown of all the channels within the sample while 6.5(b)

shows the distribution for tau + jets events when compared to the modes where no truth

hadronic tau is present. Plots are normalised to unit area

are sufficiently long that a b-hadron can travel for a few mm before it decays [56],

which can therefore produce a secondary vertex displaced from the jet origin at the

point were the decay takes place. SV0 is the simplest of the ATLAS secondary

vertex taggers [69] and was considered safe for use in the 2010 data [56]. It returns a

weight for each jet which is the signed decay length significance [69] of the displaced

vertex relative to the main jet origin. The likelihood that a jet originated from a

b-quark can therefore be established by a cut on the SV0 weight. Jets possessing a

weight > 5.72 can be said to have a 50% chance of originating from a b [56]. As the

genuine tau + jets events should contain two b-jets, it was therefore required that

at least one, but no more than two, jets in a candidate event possess an SV0 weight

> 5.72. Approximately two thirds of genuine tau + jets events are expected to pass

this cut.

171

6.6.6 Trigger

During 2010 running the trigger menus used evolved with the ramping up of the

LHC machine luminosity. As a consequence, triggers varied between luminosity

periods and were different to those that had been implemented within the Monte

Carlo productions. During periods H and I the two lowest unprescaled triggers most

suitable for this analysis were EF xe40 noMu and tau16 medium xe22 noMu. The

former is chained to L2 xe30 noMu and L1 XE25 as the LVL2 and LVL1 components

respectively. For the latter the chain was built from L1 XE25. It is expected that

any events remaining after the complete set of offline selection cuts would have

passed either one or both of these triggers.

6.6.7 Cut flow and purity

After application of the pre-selection and the additional cuts, the overall semi and

dileptonic tt̄ signal selection efficiency is seen to be 4×10−3, with a signal purity for

the tau + jets channel of 63% in tt̄ events (excluding the fully hadronic decays).

Fig. 6.6 shows the cut flow for the different components of the tt̄ sample. Table 6.2

shows the number of signal and background events expected to pass the selection,

excluding QCD backgrounds, for a range of integrated luminosities. Results from

the samples generated with Pythia [40], although scaled by large factors, showed

that the size of the QCD background would be expected to be of a similar order to

the signal.

172

ProcessExpected Events

10 pb−1 26.4 pb−1 40 pb−1 100 pb−1 200 pb−1 1 fb−1

tt̄ 3.7 9.76 14.79 36.97 73.94 369.72

W+jets 0.19 0.49 0.75 1.87 3.75 18.73

Single top 0.13 0.34 0.52 1.3 2.6 12.99

Z+jets 0.03 0.09 0.14 0.34 0.68 3.42

W+bb+jets 0.02 0.07 0.1 0.25 0.49 2.47

Diboson 0 0.01 0.01 0.02 0.05 0.29

Hadronic top 0.17 0.45 0.68 1.71 3.42 17.11

Total background 0.55 1.45 2.2 5.5 10.99 55.01

Table 6.2: Number of Monte Carlo signal and background events expected to pass the

selection for a range of integrated luminosities (excluding QCD backgrounds)

173

Cut

Prio

r to

cuts

Tau

requ

irem

ent

Miss

ing

Et

Jet m

ultip

licity T

jet P

th 4

T je

t Prd 3

Lept

on v

eto T

Scal

ar E

requ

irem

ent

TM

B-ta

g

Arbr

itrar

y Un

its410

510

610

Cut

Prio

r to

cuts

Tau

requ

irem

ent

Miss

ing

Et

Jet m

ultip

licity T

jet P

th 4

T je

t Prd 3

Lept

on v

eto T

Scal

ar E

requ

irem

ent

TM

B-ta

g

Arbr

itrar

y Un

its410

510

610 - 1 tautDL t - 2 tautDL t - 1 tautSL t - No tautDL t - No tautSL t

- 1 tautDL t - 2 tautDL t - 1 tautSL t - No tautDL t - No tautSL t

Figure 6.6: Cut flow for non-hadronic tt̄ events passing the complete event selection,

broken down into the sample components. Numbers shown are for the complete Monte

Carlo sample totaling 773167 events

6.7 Cross Section Measurement and QCD Back-

ground Estimation

The tt̄ cross section can be calculated via a counting experiment by use of the

equation;

σtt̄ =NData − NBackground

εL (6.2)

where NData is the number of events observed in a chosen signal region, NBackground

is the number of background events in that region (estimated via a combination of

Monte Carlo and data driven methods), ε is the efficiency with which signal events

are expected to be selected in that region (estimated from Monte Carlo) and L is

the integrated luminosity of the data sample.

174

6.7.1 Hadronic Top Mass Reconstruction

Having selected the tau + jets channel events, it is possible to reconstruct the

top which decays hadronically. A common technique for doing this is to form the

three jets in the event which possess the highest combined three jet pT [70]. This

procedure has been demonstrated to find the correct combination in approximately

35% of lepton + jets events [70]. This distribution is shown in Fig. 6.7 for the Monte

Carlo tt̄ signal and Monte Carlo backgrounds (excluding QCD) when scaled to an

integrated luminosity of 26.4 pb−1.

[MeV]jjjM0 50 100 150 200 250 300 350 400 450 500

310×

-1Ev

ents

/ 26

.4 p

b

00.20.40.60.8

11.21.41.61.8

[MeV]jjjM0 50 100 150 200 250 300 350 400 450 500

310×

-1Ev

ents

/ 26

.4 p

b

00.20.40.60.8

11.21.41.61.8

ttW + jetsSingle top

+ jetsbWbDiboson

tHadronic tZ + jets

ttW + jetsSingle top

+ jetsbWbDiboson

tHadronic tZ + jets

Figure 6.7: mjjj distribution for the highest combined three jet pT in non-hadronic tt̄

events and main backgrounds with the exception of QCD. Normalised to 26.4 pb−1

175

6.7.2 Defining signal region and data driven estimate of

QCD background

By reconstructing the hadronic top in the selected events, it was possible to use a

window around the top mass (currently measured as mt = 172.0±0.9±1.3 GeV [9])

to obtain a value for NData. In order to estimate the QCD contribution to this

region, the number of events was examined in the signal region in a QCD enriched

sample and then subtracted from NData after normalising to a sideband in the mass

distribution and correcting for any signal found in the diluted sample.

To produce a sample containing a QCD enriched three jet mass (mjjj) distribution

it was necessary to find a variable which, when adjusted, would alter the propor-

tion of QCD and signal in the top mjjj plot but without altering the shape of the

distributions. This was achieved through the SV0 b-tag used as the last step of the

selection procedure. Shown in Fig. 6.8 are the plots of mjjj for the signal, taken from

the Monte Carlo, for the usual described b-tagged selection in 6.8(a), and for an anti

b-tagged selection in 6.8(b). The anti-tagged selection shown in 6.8(b) used exactly

the same cuts, but with events required to fail the final b-tag contraint. As can be

seen the shapes of the distributions are roughly consistent, with the ratio of anti-

tagged to tagged events being approximately 0.4. In order to check the same was

true for the background, the equivalent plots were produced for the data as shown

in Fig. 6.9. The missing ET selection used to produce these plots was changed from

the standard >50 GeV cut, to requiring missing ET to lie in the window 20 < EmissT

< 30 GeV so as to select a sample highly populated by QCD. The fact that the

176

tagged and anti-tagged background shapes shown in Fig. 6.9 are the same is impor-

tant as it the assumption that the b-tag does not alter the shape which is used in

the method proposed for accounting for the QCD background in the signal.

[MeV]jjjM0 50 100 150 200 250 300 350 400 450 500

310×

-1Ev

ents

/ 26

.4 p

b

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6B-Tagged

(a)

[MeV]jjjM0 50 100 150 200 250 300 350 400 450 500

310×

-1Ev

ents

/ 26

.4 p

b

0

0.1

0.2

0.3

0.4

0.5

0.6Anti-Tagged

(b)

Figure 6.8: Monte Carlo distributions for mjjj possessing the highest combined three jet

pT in non-hadronic tt̄ events for SV0 b-tagged 6.8(a) and anti-tagged 6.8(b) selections.

Plots are normalised to 26.4 pb−1

To calculate the cross section and carry out the subtraction of the QCD background,

plots of mjjj were produced for the standard tagged selection and in addition for the

anti-tagged events. A window around the top mass peak from 100 GeV to 250 GeV

was defined to be used to measure NData in the b-tagged plot. A sideband region,

where the tt̄ contribution is expected to be negligible was also defined from 400 GeV

to 500 GeV. Although the contribution of the signal in the sidebands was expected

to be negligible, the strength of the cuts required to suppress the QCD contribution

before the b-tag meant that the contribution from tt̄ in the signal region of the

antitag distribution was non-negligible. This therefore had to be taken into account

177

[MeV]jjjM0 50 100 150 200 250 300 350 400 450 500

310×

Even

ts

0

20

40

60

80

100 B-Tagged

(a)

[MeV]jjjM0 50 100 150 200 250 300 350 400 450 500

310×

Even

ts

0

100

200

300

400

500Anti-Tagged

(b)

Figure 6.9: Data distributions for mjjj possessing the highest combined three jet pT after

the complete SV0 b-tagged 6.9(a) and anti-tagged 6.9(b) selections but for the requirement

20 < EmissT < 30 GeV. The integrated luminosity was 26.4 pb−1

as part of the background subtraction procedure. It was possible to parameterise the

tt̄ and QCD contributions in the tagged and anti-tagged samples as per Fig. 6.10.

(a) B-tagged (b) Anti-tagged

Figure 6.10: Schematic diagrams illustrating the variable assignment in the SV0 B-

tagged 6.10(a) and anti-tagged 6.10(b) samples for the signal and sideband regions

178

Here TS, TB, AS and AB are the number of events observed in the signal and side-

band regions for the tagged and anti-tagged samples. S is the number of tt̄ events

present in the signal region of the tagged distribution and B is the number of QCD

background events in the same region. A is the number of QCD events in the signal

region of the anti-tagged sample. f represents the ratio of QCD in the signal region

to the sideband region, which is the same for both the tagged and anti-tagged cases.

Of the variables, TS, TB, AS and AB are measured from the data plots, the ratios a,

b and ccan be extracted from the tt̄ Monte Carlo and S, B, Aand f are unknowns.

The measureables TS, TB, AS and AB can be expressed in tems of the other variables

by;

TS = S + B (6.3)

TB = aS + fB (6.4)

AS = bS + A (6.5)

AB = cS + fA. (6.6)

Fig. 6.8 shows the distributions for the tagged and anti-tagged tt̄ samples, given

by the tt̄ Monte Carlo, normalised to 26.4 pb−1. These plots show that the sig-

nal contribution to the sideband region is expected to be negligible in both cases.

179

Neglecting the signal contributions in the sidebands therefore allows equations 6.4

and 6.6 to be simplified to;

TB = fB (6.7)

AB = fA. (6.8)

It is possible to define a new variable, NCalc, which is given as;

NCalc = NData − NScaledAnti−Tag. (6.9)

Taking NData as TS, the number of events measured in the signal region of the b-

tagged plot, and NScaledAnti−Tag as the number of anti-tagged events in the same region

scaled by the ratio of the events seen in the sidebands, it is possible to write;

NCalc = TS −TB

AB

AS = (S + B) −(

fB

fA

)

(bS + A) (6.10)

and therefore rearranging;

NCalc = TS −TB

AB

AS = S

(

1 − bB

A

)

. (6.11)

Consequently, by using 6.7 and , the number of non-QCD events, S, in the signal

region of the b-tagged sample can be expressed as;

180

S =

(

TS − TB

AB

AS

)

(

1 − b TB

AB

) . (6.12)

Running over the ATLAS data periods H and I, the mjjj distributions produced for

the tagged and anti-tagged samples are shown in Fig. 6.11. Reading off the number

of events in each distribution for both the signal and sideband regions produced the

numbers shown in table 6.3.

[MeV]jjjM0 50 100 150 200 250 300 350 400 450 500

310×

Even

ts

0

1

2

3

4

5

6

7B-Tagged

(a)

[MeV]jjjM0 50 100 150 200 250 300 350 400 450 500

310×

Even

ts

0123456789

Anti-Tagged

(b)

Figure 6.11: Data distributions for mjjj possessing the highest combined three jet pT after

the complete SV0 b-tagged 6.11(a) and anti-tagged 6.11(b) selections. The integrated

luminosity was 26.4 pb−1

The statistical errors were produced by taking each of TS, TB, AS and AB to be the

mean value of a poisson distribution. The uncertainties were then formed using a

68% confidence interval on the mean value.

A value for b was produced by taking the ratio of the events in the signal region

for the tagged and anti-tagged samples, via the non luminosity-scaled version of the

181

Region Events

TS 31+6.6−5.5

TB 3+2.9−1.6

AS 46+7.8−6.8

AB 6+3.6−2.4

Table 6.3: Number of events produced in data for the signal and sideband regions for

tagged and anti-tagged selections. Integrated luminosity totaled 26.4 pb−1

plots shown in Fig. 6.8. This gave a value for b of 0.399 ± 0.015.

In order to produce a value for S the measured numbers from table 6.3 together

with the value for b were substituted into equation 6.12, yielding a value for S of 10

events. To estimate the statistical error on the value, a toy Monte Carlo was used

to carry out a large number of pseudo-experiments where TS, TB, AS and AB were

all taken as input mean values of four poisson distributions. A random generator

was used in each pseudo-experiment to produce new values for TS, TB, AS and AB

which were combined with b to produce a new value for S. After many experiments,

a 68% confidence band was applied to the resulting distribution for the generated

values of S. Reading off the upper and lower values of the interval resulted in a

measurement of S of 10+15−32 events. As can be seen, a statistical error of the order of

between 150 and 300% is produced on S, which is a direct consequence of the small

number of events seen in the data in the sideband region for both the b-tagged and

anti-tagged (background enriched) distributions.

The statistical error on S is such that it is not possible to produce a statistically

182

significant measurement of σtt̄ via this channel with the current ATLAS dataset. A

‘nominal’ value of the cross-section was still calculated however, so as to demonstate

the method. The value S represents the number of non-QCD events in the top signal

window. Consequently, the equation for calculating the tt̄ non all hadronic cross-

section given in 6.2 can be re-written as;

σtt̄ =S − ΣNNon−QCD

Background

εL (6.13)

where ΣNNon−QCDBackground is the sum of the non-QCD backgrounds, which are small and

were taken from Monte Carlo for the signal region. These are shown in table 6.4.

Process Expected Events / 26.4 pb−1

W+jets 0.12

Single top 0.15

Z+jets 0.09

W+bb+jets 0.07

Diboson 0.01

Hadronic top 0.32

Total background 0.76

Table 6.4: Number of Monte Carlo non-QCD background events expected to pass the

selection for an integrated luminosities of 26.4 pb−1

The efficiency ε for non-hadronic tt̄ events to pass the selection cuts and end up in

the signal region of the tagged mjjj plot was also calculated from Monte Carlo via

Fig. 6.8(a) and was found to be 3.1 × 10−3 ± 0.1 × 10−3, where a binomial error is

183

assumed. The luminosity L was taken from machine parameters [71] where recent

measurements have put the error on the luminosity scale during 2010 at ±3.4% [71].

Combining everything together, a value for the tt̄ non-fully hadronic cross sec-

tion × BF (where BF is the branching fraction), was produced of;

σtt̄ × BFNon all hadronic = 113+183−390pb (6.14)

It should be noted that this measurement is taken for an efficiency that, while

enriched in tau + jets, is calculated for a mixture of tt̄ channels. Ultimately, once

the measurement became statistically valid it would be necessary to subtract the

contribution from the other modes (preferably via use of consistent measurements

of those channels) and so hence forth obtain a value for the pure t → τ cross section.

Scaling the non-fully hadronic value produced here by the theoretical branching

fraction from the Monte Carlo of 0.543, a nominal value for the total tt̄ cross-section

is found to be;

σtt̄ = 207+337−718pb (6.15)

As discussed, the statistical error on S means that it is not possible to claim a

measurement of σtt̄ via this method with the 26.4 pb−1 of data taken during 2010.

However, as the values calculated forS and σtt̄ produce an output of the correct

order expected it is possible to carry out a simple extrapolation to estimate whether

184

a measurement would become achievable in the near future for ATLAS. Table 6.5

gives an estimate of how the errors on S would be expected to evolve with luminosity.

Here S, TS, TB, AS and AB have been simply scaled by appropriate factors to account

for the luminosity scaling, with the statistical error on S again calculated in the form

of a 68% confidence band via the toy Monte Carlo.

Value Events/26.4 pb−1 Events/200 pb−1 Events/500 pb−1 Events/1 fb−1 Events/3 fb−1

S 10+15−32 76+44

−26 189+84−99 379+111

−139 1135+220−227

Table 6.5: Projected evolution of S with increasing luminosity, assuming a simple upscaling

of the values for TS, TB, AS and AB

It can be seen that once 500 pb−1of data have been collected the 68% confidence band

representing the statistical uncertainty on S has become of approximately the same

order of magnitude as the signal. Thus, with an unimproved technique it is possible

to achieve an approximate two standard deviation significance for 500 pb−1of data.

Once 3 fb−1 have been collected this uncertainty band reduces to approximately

40% of the extrapolated value of S, thus corresponding to a fractional statistical

error of 20%. Thus a measurement of σtt̄ via the method described would begin

to become statistically feasable once ATLAS has collected of the order of 1 fb−1

to 3 fb−1 of data. This is expected to be achieved during the course of the current

2011 - 2013 LHC run. With refinements to the analysis techniques, discussed in 6.7.4

it is possible that a result could be produced earlier.

185

6.7.3 Systematic uncertainty on the efficiency

As has been seen, for the immediate future any attempted measurement of the tt̄

cross section from the tau + jets decay channel is likely to be limited by the size of the

statistical error. Nevertheless, as the efficiency ε is calculated directly from Monte

Carlo in this analysis, it is interesting to obtain a first estimate of the magnitude of

the systematic error on ε for when the amount of available data has increased. Some

of the expected main sources of systematic error on ε were therefore examined.

Jet Energy Scale

The analysis described uses a selection which relies on jet pT cuts, a scalar sum of jet

energies and a large missing ET cut. With the efficiency ε being taken entirely from

Monte Carlo, a potential source of systematic uncertainty exists due to deviations

between the simulated and actual jet energies measured by the ATLAS detector.

During 2010 running, it was estimated that the error on the ATLAS jet energy scale

lay in the region of 5%, with a slight variation observed as a function of pT and η

[72]. For the jet pT range of interest for this measurement (approximately 20 GeV

to 80 GeV) this was expected to be closer to the order of 5%. The effects of a 5%

uncertainties in the jet energy scale (JES) was therefore considered.

One way of simulating a shift in the JES would be to fully rescale all the jet can-

didates before any analysis was carried out by ± a chosen scale factor, including

recalculating the missing ET. In this case the energy scale shift was studied by

186

simultaneously shifting of the cuts dependent on the jet energy. This included as-

suming the hadronic tau energy scale to also have an uncertainty equivalent to that

of the main JES. For example, to represent a 5% underestimation of the JES, the

jet pT, tau pT and missing ET cuts were all lowered by 5%, as were the upper and

lower bounds of the top mjjj signal region, while the scalar ET and transverse mass

cut values were increased by 5%. This adjustment included the cuts used in the

object preselections. Table 6.6 shows the effect of the ±5% JES uncertainties on the

efficiency.

JES shift ∆ε/ε

+5% -33%

-5% +42%

Table 6.6: Fractional uncertainty on the efficiency as a result of a ±5% shift in the jet

energy scale

It can be seen that a 5% shift in the JES as modelled here produces a very significant

fractional error on ε. However, the scaling technique used means that this is possibly

a conservative estimate (for example missing ET is not calculated entirely from jets

but is still scaled up by the same amount). Furthermore, while the current estimate

of the JES uncertainty is of the order of 5%, this will improve as the detector is

better understood, with the aim for ATLAS ultimately to have a JES uncertainty

of 1% [35]. At the same time aspects of the analysis could be considered so as to

try and reduce the sensitivity to the JES. One possible way of doing this would be

to try and loosen some of the jet based cuts.

187

Monte Carlo Modelling

The Monte Carlo tt̄ dataset used as the default throughout the course of this analysis

was as per that described in 6.2 where the generators used were MC@NLO (to

provide the matrix element) and Herwig/Jimmy to provide the parton showering.

The PDF CTEQ6.6 was also used. To examine the effect of different generator/PDF

sets, the efficiency was recalculated for two new datasets, both of which simulated the

non-fully hadronic tt̄ with decays to electons, muons and tau final states allowed.

The first sample considered 3 used a matrix element provided by POWHEG [73]

with parton showering provided via Herwig [41] and PDF based on CTEQ6L1 [74].

A fractional difference for the efficiency calculated via this dataset compared to

the default was seen to be +6%. The second control sample considered 4 used

AcerMC [75] to provide the matrix element with Pythia [40] giving the parton shower

and the PDF used was based on the MRST [76] case. Recalculating the efficiency for

this sample produced a fractional difference when compared to the main Monte Carlo

of +1%. Although there are many different PDF sets and generators which could

be examined, these two results show that the systematic error on the tt̄ efficiency

would be expected to be of the order of 5%.

3mc09 7TeV.105860.TTbar PowHeg Jimmy.merge.log.e540 s765 s767 r1302 r13064mc09 7TeV.105205.AcerMCttbar.merge.log.e552 s765 s767 r1302 r1306

188

Matrix Element Parton Shower PDF Type ∆ε/ε

POWHEG Herwig CTEQ6L1 +6%

AcerMC Pythia MRST +1%

Table 6.7: Fractional uncertainty on the efficiency for two different generator and PDF

combinations

Top Quark Mass

The tt̄ efficiency is calculated based on the fraction of events ending up in the 100-

250 GeV mass window of the mjjj plot. As a consequence of this it could be sensitive

to systematic shifts in the location of the top mass peak. In addition, many of the

cuts used in the event preselection would also be sensitive to a shift in the top mass

as it would be expected to have an effect on the energy spectra of the top decay

products. To test this a series of samples were available which were simulated with

the same generator settings as per the standard samples, but for a range of different

top masses. Table 6.8 shows the fractional change in the efficiency as a result of

changing the top mass (compared to the 172.5 GeV mass of the standard tt̄ sample)

by +2.5−5 GeV. As the current statistical and systematic errors on the measured top

mass at the TeVatron are each of the order of ±1 GeV [9] this is a conservative

estimate.

As the TeVatron experiments have measured the real value of the top quark mass to

an accuracy of the order 1-2 GeV, then it is unrealistic to use the complete fractional

error given by the 5 GeV shift as part of an overall systematic error calculation. From

the size of the uncertainty produced by the +2.5 GeV shift, it would be reasonable

189

Mass Shift ∆ε/ε

+2.5 GeV +7.5%

-5.0 GeV -19%

Table 6.8: Fractional uncertainty on the efficiency as a result of a shift in the top quark

mass

to expect a variation on ε to be of the order of 10% for a -2.5 GeV shift in the top

mass.

B-tagging efficiency

The SV0 b-tag used in the analysis as set was expected to give a b-jet efficiency

of 0.497. The efficiency was recalculated for SV0 weights of 9.08 and 0.08 which

correspond to b-jet efficiencies of 0.405 and 0.576 respectively. In data, for 25

< pT(jet) < 85 GeV the b-jet tagging efficiency is expected to vary from 40% to

60% [56]. Table 6.9 gives the fractional errors on ε as a result of the variation in the

b-jet tagging efficiency.

b-jet efficiency ∆b-jet efficiency ∆ε/ε

0.576 +7.9% +7.48%

0.405 -9.2% -14.76%

Table 6.9: Fractional uncertainty on the efficiency as a result of a shift in the b-tagging

efficiency

190

Tau Identification

The tau ID used relied on a single cut on the EmRadius of the tau candidate. This

was set to correspond to a hadronic tau selection efficiency in Monte Carlo of 30%.

The EmRadius cuts the for 1-Prong candidates (3-Prong candidates were not used)

were varied so as the tau selection efficiency varied by ±10% This was a deliberately

conservative estimate. This resulted in a variation of the tt̄ efficiency of;

Tau ID efficiency ∆tau ID efficiency ∆ε/ε

0.40 +10% +22.58%

0.20 -10% -26.82%

Table 6.10: Fractional uncertainty on the efficiency as a result of a ±10% shift in the tau

selection efficiency

Monte Carlo Statistics

Non-QCD backgrounds were subtracted from S using Monte Carlo predictions only.

As such there is a systematic uncertainty associated with the Monte Carlo statistics

available for these samples. Adding the uncertainties for the samples in quadrature,

an overall uncertainty was produced of approximately ±20% where the dominant

uncertainty was on the measurement of the W+jets background. The overall system-

atic error on the non-QCD background subtraction could be reduced by attempting

to estimate some of these backgrounds from data.

191

Overall Errors

In order to obtain a conservative estimate for the total overall systematic on ε,

the individual systematics were combined by adding the positive uncertainties in

quadrature and then repeating for the negative uncertainties. The values combined,

together with the total calculated uncertainty are shown in table 6.11. In addition to

the systematic uncertainty on ε, subtraction of Monte Carlo backgrounds contribute

an uncertainty of ±20%, while the ATLAS luminosity error during 2010 was of the

order ±3.4% [71].

Source Uncertainty (%)

JES +42−32

Generator/PDF +6−6

Top Mass +7.5−10

B-Tag +7−14

Tau ID +22−26.8

Total uncertainty +53−50

Table 6.11: Systematic uncertainties on the efficiency ε for selecting tt̄ events via the

method described

As can be seen, the overall systematic uncertainty is large (±50%) in the current

analysis and is dominated by the uncertainties due to the jet energy scale and the

tau identification. However, there are ways in which it is believed that these could

be improved with time. Firstly, as mentioned reducing the size of the uncertainty

on the JES is a significant aim for ATLAS. It would be hoped that this would fall

192

as ATLAS running progresses from around 5% to approximately the design target

value of 1% [35], leading to an automatic drop in the size of the associated systematic

error. More sophisticated analysis techniques could also be applied in time so as to

reduce the sensitivity to the JES. This would envolve trying to identify those cuts

which were most sensitive to the JES and adjusting them so that the effect became

less drastic. Once sufficient statistics became available a logical way to do this would

be to look at fitting the mass distributions. This would make better use of a given

set of statistics and also have the additional effect of reducing the reliance on the

number of events in the sideband regions. The 10% shift in the tau identification

efficiency applied is conservative, however one way in which the sensitivity to this

could be reduced would be to use Z → ττ to try and measure the tau identification

efficiency in data when sufficient luminosity becomes available. More sophisticated

methods of tau identification than the single variable cut used here would also be

likely to help reduce the systematic uncertainty, whilst hopefully also allowing some

of the other cuts to be loosened, improving the overall tt̄ efficiency. Similarly, if a

way could be found to measure some of the other Monte Carlo backgrounds, such

as the W+jets, from data then the uncertainty on the Monte Carlo background

subtraction could also hopefully be reduced. Over time it would also be reasonable

to assume that the performance of the available b-taggers should improve and hence

reduce the systematic error accordingly.

193

6.7.4 Future prospects

As was described in 6.7.1, statistics in the background control regions meant that it

was not possible to make a significant measurement of the tt̄ cross section with the

2010 data. However, table 6.5 when combined with the expected systematic errors

on ε and possibilities for improving them show that a measurement will be possible

within the current 2011-2013 LHC run. Advancement in analysis techniques such as

fitting distributions and possibly using multivariant techniques for tau identification

could reduce the period of time this would take providing the systematics could be

controlled. It is therefore possible to consider how the analysis could be evolved in

the near future. Firstly, this chapter discussed a method to measure the overall tt̄

cross section. However a more interesting figure to study is the branching fraction

for tt̄ to tau decays as this is where the presence of any new physics, such as a light

charged Higgs boson, is likely to appear. Therefore, once sufficient data was available

a useful measurement to make would be to make a measurement of the cross section

times the branching fraction to taus. Comparing this to similar measurements for

muons and electons in tt̄ events would therefore provide both a cross check of the

standard model and a probe for potential new physics.

6.8 Conclusion

Observing the decay of a tt̄ pair to tau + jets is a substantial challenge at a hadron

collider due to the nature of the final state. A method was proposed, which de-

194

liberately avoided sophiticated multivariant techniques in favour of simple cuts, to

attempt to measure the tt̄ cross section via this channel, using early data from the

ATLAS detector at the LHC. The analysis was developed on Monte Carlo events and

then applied to 26.4 pb−1of 2010 ATLAS data. A series of deliberately simple cuts

were used for event selection, and a cut and count technique used to estimate the

number of tt̄ events in a window around the hadronic top mass peak. A subtraction

of QCD background from data was performed by scaling a number of events from

a QCD enriched sample by the ratio of events in a sideband region of the hadronic

top mass. It was established that with the current available dataset a statistical

error is expected of the order of ±400% and thus a measurement is not feasible at

this stage. The systematic error on the tt̄ selection efficiency was conservatively

estimated to be of the order of ±50%. However, it was established via a simple

luminosity scaling that a measurement should become statistically possible within

the period of the current 2011-2013 LHC run, while a few suggestions were made as

to how the systematic uncertainty on the efficiency could be reduced.

195

Appendix A

pT[GeV] CutLevel EmRadius StripWidth2 IsolationFraction EnergyRatio

10-25

Loose ≤0.11 ≤0.047 ≤0.75 ≤1.02

Medium ≤0.072 ≤0.045 ≤0.65 ≤1.02

Tight ≤0.055 ≤0.033 ≤0.32 ≤1.01

25-45

Loose ≤0.087 ≤0.048 ≤0.89 >0.0010

Medium ≤0.058 ≤0.043 ≤0.24 >0.0011

Tight ≤0.048 ≤0.0030 ≤0.20 >0.023

45-70

Loose ≤0.081 ≤0.050 ≤0.31 >0.00040

Medium ≤0.050 ≤0.035 ≤0.26 >0.00040

Tight ≤0.037 ≤0.035 ≤0.26 >0.0028

70-100

Loose ≤0.150 ≤0.040 ≤0.70 >0.0010

Medium ≤0.045 ≤0.036 ≤0.14 >0.029

Tight ≤0.045 ≤0.015 ≤0.058 >0.029

>100

Loose ≤0.500 ≤0.030 ≤0.60 >0.00033

Medium ≤0.034 ≤0.030 ≤0.60 >0.00033

Tight ≤0.034 ≤0.00069 ≤0.049 >0.0015

Table A.1: Calorimeter only safe cut values for identification of 1-prong hadronic taus [53]

196

pT[GeV] CutLevel EmRadius StripWidth2 IsolationFraction EnergyRatio

10-25

Loose ≤0.21 ≤0.057 ≤0.96 ≤1.02

Medium ≤0.15 ≤0.056 ≤0.90 ≤1.02

Tight ≤0.096 ≤0.048 ≤0.62 ≤1.01

25-45

Loose ≤0.15 ≤0.045 ≤0.79 ≤1.01

Medium ≤0.088 ≤0.044 ≤0.68 ≤1.01

Tight ≤0.068 ≤0.044 ≤0.42 ≤1.01

45-70

Loose ≤0.25 ≤0.031 ≤0.25 ≤1.08

Medium ≤0.071 ≤0.031 ≤0.25 ≤1.03

Tight ≤0.053 ≤0.026 ≤0.25 ≤1.01

70-100

Loose ≤0.23 ≤0.036 ≤0.50 ≤1.02

Medium ≤0.061 ≤0.035 ≤0.20 ≤1.01

Tight ≤0.048 ≤0.035 ≤0.18 ≤1.00

>100

Loose ≤0.071 ≤0.038 ≤0.47 ≤1.00

Medium ≤0.061 ≤0.037 ≤0.20 ≤1.00

Tight ≤0.036 ≤0.030 ≤0.18 ≤0.99

Table A.2: Calorimeter only safe cut values for identification of 3-prong hadronic taus [53]

197

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